How do I finals out the arithmetic from the geometric

Question

the sum of three consecutive terms of an arithmetic sequence is 30 when these terms are increased by 2,5 and 28 respectively. the resulting numbers are a geometric sequence. determine the terms?

Answer 1

a + a+d + a+2d = 30

 

a+2, a+d+5, a+2d+28 are three consecutive terms of a Geometric Sequence.

 

r(a+2) = a+d+5

r(a+d+5) = a+2d+28 

 

Now you have three equations in three unknowns (a, d, r).

 

SOLVE THE SYSTEM!