Question

The sum of this geometric series with 7 terms: 2 + 6 + ... + 1458 is

Answer 1

Answer: The required sum is 2186.

Step-by-step explanation: We are given to find the sum of the following geometric series with 7 terms:

`2+6+~.~.~.~+1458.`

We know that the sum of a geometric series up to 'n' terms with first term 'a' and common ratio 'r' is given by

`S=(a(r^n-1))/(r-1).`

In the given geometric series, we have

first term, a = 2

and the common ratio 'r' is

`r=(6)/(2)=3.`

Also, n = 7.

Therefore, the sum of the given series is

`S\\\\\\=(a(r^n-1))/(r-1)\\\\\\=(2(3^7-1))/(3-1)\\\\\\=(2(2187-1))/(2)\\\\\\=2186.`

Thus, the required sum is 2186.

Answer 2

The sum of the terms in a geometric sequence is obtained through the equation below,
S = (a1)(1 - r^n)/(1 - r)
Substituting,
S = 2(1 - 3^7) / ( 1 - 3) = 2186
Thus, the sum of the first 7 terms in the geometric sequence is equal to 2186.