(K:1) Find S8 for the series 3+15+75+375+…

Question

BlackTom AI · Accepted Answer

The series 3, 15, 75, 375, … is a geometric progression with first term a1 = 3 and common ratio r = 5. To find S8 (the sum of the first 8 terms), use the geometric series sum formula: S_n = a1 * (r^n − 1) / (r − 1).

Compute r^n: 5^8 = 390,625.
Subtract 1: 390,625 − 1 = 390,624.
Multiply by a1: 3 * 390,624 = 1,171,872.
Divide by (r − 1): 1,171,872 / 4 = 292,968.

Thus S8 = 292,968. Now evaluate each option:

Option a: 724. This is far too small for a sum that grows by a factor of 5 each term; it does not reflect the rapid growth of the sequence.

Option b: 38. This value is also far too small and does not account for the repeated multiplication by 5 across eight terms.

Option c: 292,968. This matches the correct calculation from the geometric sum formula and aligns with the sequence’s rapid growth.

Option d: 97,656. This is smaller than the true sum; it might correspond to summing fewer terms or missing a factor, but it does not equal the eight-term sum.

In short, recognizing the pattern as a geometric progression and applying the sum formula yields the correct total, while the other numbers fail to reflect the compounded growth across eight terms.

(K:1) Find S8 for the series 3+15+75+375+…

View Explanation

Log in for full answers

Similar Questions

Question12 Consider the series [math]. Which of the following correctly says what the series is equal to on its interval of convergence?Select one alternative: [math] [math] [math] [math] ResetMaximum marks: 1 Flag question undefined

What is the first term of the geometric series with and ? (type number only into box)

What would be the sum of the first 18 terms of the geometric series with: 20 1.4 (type answer only in box correct to the nearest whole number)

What is the sum of the series \[(-1/3)^0+(-1/3)^1+(-1/3)^2+(-1/3)^3+\ldots\] Remember to enter your answer in lowest terms.

What is the sum of the series [math: (−1/3)0+(−1/3)1+(−1/3)2+(−1/3)3+…](-1/3)^0+(-1/3)^1+(-1/3)^2+(-1/3)^3+\ldots Remember to enter your answer in lowest terms.

The sum to infinity of a geometric sequence is 20 and the common ratio r is 0.2. What are the first four terms of the sequence?

The sum of the first seven terms of the geometric sequence: 0.2, 0.8, 3.2, … is closest to:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler