Chapter 8, Problem 29CR

To determine

Find the explicit rule for the given sequence.

Answer to Problem 29CR

Theexplicit rule for the given arithmetic sequence is $a_n=-4+\left(n-1\right)26$ .

Explanation of Solution

Given:

The given datais $a_1=-4$ , $a_n=a_{n-1}+26$ .

Calculation:

The recursive rule for an arithmetic sequence is $a_n=a_{n-1}+d$

The recursive rule represents an arithmetic sequence with first term $a_1=-4$ and the common difference $d=26$ .

The explicitrule for the arithmetic series is $a_n=a_1+\left(n-1\right)d$ .

Substitute the value of $a_1=-4$ and the common difference $d=26$ .

in the explicit rule.

  $a_n=-4+\left(n-1\right)26$

Hence the explicit rule for the given arithmetic sequence is $a_n=-4+\left(n-1\right)26$ .