Question

An arithmetic and a geometric sequence have the same first terms.(2)....and the same second term say X..The sum of the first 3 terms of the arithmetic sequence equals to the third term of the geometric sequence.Calculate the first 3 terms of each sequences

Answer 1

a+d = ar
3/2 (2a+2d) = ar^2
3a+3d = ar^2
3(a+d) = ar^2
3ar = ar^2
3r = r^2
r = 3

So,
a+d = 3a
d = 2a

The sequences are thus
a,3a,5a,7a,9a,...
a,3a,9a,27a,...
Note that a+3a+5a = 9a, as required

Pick a value for a, and plug and chug.