Question

Find the sum of the first five terms of the geometric series 1+3+9+...

Answer 1

Good evening ,

Answer:

B. 121

Step-by-step explanation:

1×3=3

3×3=9

9×3=27

27×3=81

the sum = 1+3+9+27+81 = 121.

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Answer 2

The sum of $1^{st}$ five terms of the series is 121.

Option - B

SOLUTION:

Given that, we have to find the sum of the first five terms of the geometric series 1 + 3 + 9 + ...  

We already know, first three terms, let us find next two terms also.

$\text { Then, common ratio }=\frac{\text { second term of series }}{\text { first term series }}=\frac{3}{1}=3$

Now, we know that, $4^{th}$ term is $3^{rd}$ term multiplied by the common ratio so, $4^{\text {th }} \text { term }=9 \times 3 \rightarrow 4^{\text {th }} \text { term }=27$

And, $5^{th}$ term is $4^{th}$ term multiplied by common ratio. So, $5^{\text {th }} \text { term }=27 \times 3 \rightarrow 5^{\text {th }} \text { term }=81$

Now, sum of first five terms = $1 + 3 + 9 + 27 + 81 = 4 + 36 + 81 = 40 + 81 = 121$

Hence, the sum of $1^{st}$ five terms of the series is 121.