131k views
1 vote
Find the sum of the first five terms of the geometric series in which a₂ is -12 and a₅ is 768

a) -3720
b) 3720
c) 1920
d) -1920

1 Answer

2 votes

Final answer:

To find the sum of the first five terms of a geometric series with given second and fifth terms, calculate the common ratio and the first term of the series, then apply the sum formula for a geometric series.

Step-by-step explanation:

The question asks to find the sum of the first five terms of a geometric series. Given a₂ (the second term) is -12 and a₅ (the fifth term) is 768, we can use the formula for the nth term of a geometric series, which is aᵢ = a₁r¹⁸⁴, where aᵢ is the nth term, a₁ is the first term, and r is the common ratio. To find the common ratio, we use the fact that a₅ = a₁r⁴. Dividing a₅ by a₂ gives us , and we can then calculate r.

Once r is found, we calculate a₁ from a₂ = a₁r. With a₁ and r, we can find the sum of the first five terms using the formula for the sum of a geometric series: Sₙ = a₁(1 - rₙ)/(1 - r) for n terms.

This process will lead us to the correct answer, which should match one of the provided options in the question.

User StefanQ
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.