What is the formula for the sum of the first n terms of a geometric sequence with first term a1 and common ratio r (r ≠ 1)?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $25.99Unlock all

Study for the Algebra 2 Honors Test. Prepare with flashcards and multiple choice questions, each question comes with hints and detailed explanations. Excel in your exam preparation!

Multiple Choice

What is the formula for the sum of the first n terms of a geometric sequence with first term a1 and common ratio r (r ≠ 1)?

Explanation:
The sum of the first n terms of a geometric sequence is found by writing S_n as a1 + a1 r + a1 r^2 + ... + a1 r^{n-1}. Multiply this sum by the common ratio r to align the terms: r S_n = a1 r + a1 r^2 + ... + a1 r^n. Subtract these two equations to cancel all the middle terms, leaving (1 - r) S_n = a1 (1 - r^n). Solve for S_n to get S_n = a1 (1 - r^n) / (1 - r), which is valid when r ≠ 1. (If r = 1, the sum would simply be n a1.)

The sum of the first n terms of a geometric sequence is found by writing S_n as a1 + a1 r + a1 r^2 + ... + a1 r^{n-1}. Multiply this sum by the common ratio r to align the terms: r S_n = a1 r + a1 r^2 + ... + a1 r^n. Subtract these two equations to cancel all the middle terms, leaving (1 - r) S_n = a1 (1 - r^n). Solve for S_n to get S_n = a1 (1 - r^n) / (1 - r), which is valid when r ≠ 1. (If r = 1, the sum would simply be n a1.)

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy