Question

A geometric series has a sum of 1365. Each item increases by a factor of 4. If there

are 6 terms in the series, find the value of the first term.

Answer 1

1

Explanation:

So the sum of a finite geometric series can be defined as:
`S_n = (a_1-a1*r^n)/(1-r)` where r is the constant ratio or how much more greater the current term is, compared to the previous term (how much it's being multiplied by), and the n is the number of terms in the series. So with the given information you have the equation:

`1365=(a_1-a_1*4^6)/(1-4)`

Simplify:

`1365=(a_1-4096a_1)/(-3)`

Multiply both sides by -3

`-4095 = a_1-4096a_1`

Subtract coefficients

`-4095=-4095a_1`

Divide both sides by -4095

`1 = a_1`