1. The sum of p terms of an Arithmetic Progression is q and the sum of q terms of the Arithmetic progression is p. Find the sum of (p+q) terms.
2. The Harmonic Mean of two numbers is 4. Their Arithmetic Mean A and the Gemetric Mean G satisfy the relation 2A+G²=27. Find the two numbers.
3. The value of x+y+z is 15 if a,x,y,z,b are in Arithmetic Progression while the value of 1/x+1/y+1/z=5/3 when a,x,y,z,b are in Harmonic Progression. Find a and b.
4. Find three numbers a,b,c between 2 and 18 such that (i)their sum if 25 (ii)the numbers 2,a,b are consecutive terms of an Arithmetic Progression and (iii) the numbers b,c,18 are consecutive terms of a Geometric Progression.
5. If a,b,c,d are in Geometric Progression, show that
(a-d)² = (b-c)² + (c-a)² + (d-b)².
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Find the coordinates of the intersection of
and its inverse. Do not use a calculator.