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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP#605. A sum of $700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is $20 less than its preceding prize, find the value of each of the prizes.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP#606. Show that

form an Arithmetic Progression where is defined as . Also, find the sum of the first 15 terms.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 588

a1, a2, a3 forms an A.P with d=4.

They are:

a1=7

a2= 11

a3=15

S15= 525.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi 666 bro,

Neat work!

SP # 607. Show that

form an Arithmetic Progression where is defined as Also, find the sum of the first 15 terms.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 608. The sum of 15 terms of an Arithmetic Progression with common difference 6 is 780. Write the algebraic expression of the sequence.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 609. Write the algebraic expression for the sum of the sequence.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 588

Sp#609: 2sₙ -n(2a+(n-1)d) =0

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

SP # 610. Write arithmetic sequences with 100 as the sum of the first four terms.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 588

Sp#610 the sequences are:

(1) : 10, 20, 30 , 40 where

a = 10 & d = 10.

(2) :25, 25, 25,25 where

a = 25 & d = 0.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Partially correct. Good attempt!

SP# 611. Consider an arithmetic sequence

.(a) Find the algebraic expression of the sequence.

(b) Is there any counting number in the sequence?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 588

SP#611 (a) : sₙ = ( n^2) + (10/7)n.

(b) : no,

*Last edited by 666 bro (2020-06-27 20:34:46)*

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

SP # 612. (a) What is the sum of first 20 natural numbers?

(b) The algebraic form of an arithmetic sequence is 6n + 5. Find the sum of the first 20 terms of this sequence.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 588

(a) : s₂₀ = 210.

(b) : s₂₀ = 1360.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Well done!

SP # 613. Sum of first n terms of an arithmetic sequence is 3n² + n. Find the first term and common difference of this sequence.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 588

Sp#613: a= 4 & d=6.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Good work!

SP # 614. (a) The fifth term of an arithmetic sequence is 40 and 10th term is 20. What is the 15th term?

(b) How many terms of this sequence make the sum zero?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 615. The sum of first ten terms of an arithmetic sequence is 350 and the sum of first five terms is 100. Write the algebraic expression for the sequence.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 616. What is the difference between the sum of the first 20 terms and the next 20 terms of the Arithmetic Progression 6, 10, 14, ....?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 617. The third term of an arithmetic sequence is 34 and its eighth term is 69.

(i) Find the common difference of this sequence.

(ii) Write the algebraic form of this sequence.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 618. Calculate the difference between the sum of the first 20 terms of the Arithmetic Progression 6, 10, 14, .... and 15, 19, 23, .....

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 619. Find the 13th term of an arithmetic sequence is 5 times the 5th term is equal to 8 times the 8th term.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

SP # 620. Find the sum of all three digit numbers which are a multiple of 7.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Denominator****Member**- Registered: 2009-11-23
- Posts: 184

Hello,

*Last edited by Denominator (2020-12-01 12:14:45)*

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 31,715

Hi,

Excellent!

SP#621. The first term of an Arithmetic Progression is 6 and the sum of the first 6 terms is 66.

(a) What is the 6th term?

(b) What is the common difference of the Arithmetic Progression?

(c) What are the first 6 terms of this Arithmetic Progression?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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