Question

Find a1, for the given geometric series. Round to the nearest hundredth if necessary. Sn= 86,830, r= 2.2, n=4

Answer 1

4,646.30

Explanation:

The sum of n terms of geometric sequence can be calculated using formula

`S_n=(a_1(1-r^n))/(1-r)`

In your case,

`S_n=86,830\\ \\r=2.2\\ \\n=4\\ \\a_1=?`

Substitute into the formula:

`S_4=(a_1(1-2.2^4))/(1-2.2)\\ \\86,830=(a_1(1-23.4256))/(-1.2)\\ \\-104,196=a_1(-22.4256)\\ \\22.4256a_1=104,196\\ \\a_1=(104,196)/(22.4256)\approx 4,646.30`