Question

An arithmetic progression as the same first and second terms as the geometric progression. Find the sum of the first 20 terms of the arithmetic progression.

How do I do this? I tried to find the common ratio for G.P. and then substitute it to find the 20th term but, still have 2 unknown terms. Please help!

Answer 1

first term: a
2nd term a+d and ar

so, a+d = ar
r = 1 + d/a

So, pick an a&d, say 1&2.
AP: 1,3,5,7,9...
GP: 1,3,9,27,81,...

or, 10&5:
AP: 1,11,21,31,...
GP: 1,11,121,1331,...

If no other information is given, that's about as far as we can go.