Question

How do you solve the first problem? (About the geometric series, and finding the first term and common ratio)

Answer 1

Answer:

First term = 5.

Common ratio = -3.

Step-by-step explanation:

Third term = a1 r^2 = 45. As r is an integer  3 or -3 is a possible value of r.

If r = 3 then the first term a1 = 45 / 9 = 5.

Substitute a1 = 5 and r = 3 into the formula for the sum of 7 terms which is given as 2735.  

Try r = 3:

S7  = 5 * (3^7 - 1) / (3 - 1) =   5465 so  r can't be  equal to 3.

Try r = -3:-

If r = -3 then a1 = 5 so

S7 = 5 * ((-3)^7 - 1) / (-3-1)  

= 5 *  547

= 2735 which is the value given.

So r = -3   and a1 = 5.