Question

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

Answer 1

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. 

Answer 2

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

$S=\dfrac{a(r^n-1)}{r-1}.$

In the given geometric series, we have

first term, a = 2

and the common ratio 'r' is

$r=\dfrac{6}{2}=3.$

Also, n = 7.

Therefore, the sum of the given series is

$S\\\\\\=\dfrac{a(r^n-1)}{r-1}\\\\\\=\dfrac{2(3^7-1)}{3-1}\\\\\\=\dfrac{2(2187-1)}{2}\\\\\\=2186.$

Thus, the required sum is 2186.