Question

Evaluate this equation ​

Answer 1

The correct answer is option B which is Sn = -111974.

What is geometric expansion?

When there is a constant between the two successive numbers in the series then it is called a geometric series.

Here we have the following data:-

$\sum_{n=1}^7-2.6^{n-1}$

$a_n = a_1r^{n-1}\ \ \ \ \ S_n = a_1(\dfrac{1-r^n}{1-r})$

Here we need to calculate the first term second term and common ratio to calculate the sum of the series.

a₁ = -2.(6¹⁻¹) = -2

a₂ = -2.( 6²⁻¹) = -2 (6) =-12

Common ratio:-

$a_n = a_1r^{n-1}$

$-12 = -2r^{2-1}$

r = 6

Put all the values in the sum formula:-

$S_n = -2(\dfrac{1-6^7}{1-6})$

$S_n = -2(\dfrac{279935}{5})=-2\times 55987$

$S_n$ = -111974

Therefore the correct answer is option B which is Sn = -111974.

To know more about geometric progression follow

brainly.com/question/12006112

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