Question

The first and second term of an exponential sequence are respectively the fourth and third term of a linear sequence.The fourth term of the linear sequence is 10 and the sum of it's first five terms is 60 find

a.the first five terms of the linear sequence and the sum of the first n terms.
b.the sum of the first n terms of the exponential sequence.

Answer 1

If the exponential sequence begins with a

and the linear sequence begins with b, we have
a = b+3d
ar = b+2d
b+3d = 10
5/2 (2b+4d) = 60
solve to get
a=10, r = 6/5
b=16, d = -2
The two sequences are thus
10, 12, 14.4, 17.28, 20.736 ...
16, 14, 12, 10, 8, ...
now finish off using the sum formulas you know.