Question

The first and second terms of an arithmetic and a geometric sequence respectively are the same and equal
to 12. The sum of the first two terms of the arithmetic sequence is four times the first term of the geometric
sequence and the common difference is 4. Find the first term of each sequence.

Answer 1

The first term of the arithmetic progression = 12

The common difference is '4'.

Then the progression is,

12, 16, 20, 24,.......

Second term of the geometric progression = 12

Let the common difference be 'y'.

Now the geometric progression is,

12/y, 12, 12y, 12y^2,.......

Given condition,

Sum of first two terms of arithmetic progression

                      = 4 X first term of the geometric progression

12 + 16 = 4 X (12/y)

28 = 48/y

y = 48/28 = 12/7

First term of arithmetic progression = 12

First term of geometric progression = 12/(12/7) = 7