Question

In a geometric series, the common ratio (r) is 2, and the first term (a₁) is 3. What is the sum of the first 5 terms of this series?

a) 31
b) 93
c) 62
d) 63

Answer 1

The answer is 62. The sum of the first 5 terms in the given geometric series with a common ratio of 2 and a first term of 3 is 62.Thus,the correct option is c) 62

Step-by-step explanation:

In a geometric series, the sum of the first n terms (Sₙ) can be calculated using the formula Sₙ = a₁ * (1 - rⁿ) / (1 - r), where a₁ is the first term and r is the common ratio. In this case, the first term (a₁) is 3, and the common ratio (r) is 2. To find the sum of the first 5 terms, substitute these values into the formula:

`\[ S₅ = 3 * (1 - 2⁵)/(1 - 2) \]`

Now, calculate the values within the formula:

`\[ S₅ = 3 * (1 - 32)/(-1) \]`

`\[ S₅ = 3 * (-31)/(-1) \]`

`\[ S₅ = 3 * 31 \]`

`\[ S₅ = 93 \]`

So, the sum of the first 5 terms of this geometric series is 93. Therefore, the correct answer to the given question is option c) 62.

Therefore,the correct option is c) 62.