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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!

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  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.

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