Question

Find $n$ when $a_{1}=5, d=-3,$ and $a_{n}=-76$

   Find $n$ when $a_{1}=5, d=-3,$ and $a_{n}=-76$

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 14, Problem 31

Instant Answer

Solved by Expert Julie Silva

05/27/2020

Step 1

We can use the formula for the nth term of an arithmetic sequence, which is $a_{n}=a_{1}+(n-1)d$. Show more…

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Find $n$ when $a_{1}=5, d=-3,$ and $a_{n}=-76$

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Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is applied repeatedly from the first term to generate the entire series, making it predictable and structured.

Common Difference

The common difference is the fixed amount that is added to or subtracted from each term of an arithmetic sequence to obtain the subsequent term. It is determined by subtracting any term from its following term and remains the same throughout the sequence.

Nth Term Formula

The nth term formula of an arithmetic sequence is given by a? = a? + (n - 1)d, where a? is the first term, d is the common difference, and n is the term number. This formula is used to find any term in the sequence when the first term and common difference are known.

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