Find the nth term of theanthmetic sequenceag=1612.

Name: Find the nth term of theanthmetic sequenceag=1612.
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Description: Find the nth term of theanthmetic sequenceag=1612.

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Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter12: Sequences, Series And Binomial Theorem

Section12.2: Arithmetic Sequences

Problem 12.36TI: Find the sum of the first 30 terms of the arithmetic sequence: 7, 10, 13, 16, 19, …

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Question

Find the nth term of the
anthmetic sequence
ag=16
12.

Expert Solution

Step 1

Given:

The first term of a arithmetic progression is, $a_{1} = - 4$ .

The fifth term of a arithmetic progression is, $a_{5} = 16$ .

The objective is to find the $n^{t h}$ term of the arithmetic sequence.

Step 2

The general formula of arithmetic progression is,

$a_{n} = a_{1} + (n - 1) d$

It is given that $a_{1} = - 4$ .

Then,

$\begin{array}{rcl} a_{5} & = & a_{1} + (5 - 1) d \\ 16 & = & - 4 + (5 - 1) d \\ 16 & = & - 4 + 4 d \\ 4 d & = & 16 + 4 \\ 4 d & = & 20 \\ d & = & \frac{20}{4} \\ d & = & 5 \end{array}$

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