Geometric sequences

Question

Find the sum of an eight term geometric sequence when the first term is seven and the last term is 114,688.

Answer 1

Hi Katelin,

 

Your first term in this sequence is 7. Your eighth term is 114688 = 7*4⁷. I assume that the terms in the sequence are as follows:

 

7*4⁰, 7*4¹, 7*4², 7*4³, 7*4⁴, 7*4⁵, 7*4⁶, 7*4⁷.

 

Or

 

7, 28, 112, 448, 1792, 7168, 28672, 114688

 

The sum of all 8 of these numbers is 152915 

Answer 2

In a geometric series, a common ratio is applied to each term.

No ratio was given in the data, but the ratio can be figured by noting the starting and ending numbers.

The starting number is 7, and the ending number is 114,688.

Since 7 is the starting number, we can see that the only other number, which when multiplied by 7 yields an 8 in the product is 4.

 

Thus, the terms are 7, 28, 112, 448, 1792, 7168, 28672, 114688

We can simply add those numbers, or use the formula

Sum  = a1((1 + rⁿ)/(1 + r))

In either case, we get 152,915