Chapter 11.2, Problem 80HP

To determine

Prove the formula for the nth term of an arithmetic sequence.

Answer to Problem 80HP

  $a_n=a_1+(n-1)·d$ Proved

Explanation of Solution

Given:

Prove the formula for the nth term of an arithmetic sequence.

Concept Used:

Let $a_n$ = the nth term of the sequence and d is the common difference.

Calculation:

Let $a_n$ = the nth term of the sequence and d is the common difference.

  $a_2=a_1+d$ The definition of the second term of an arithmetic sequence

  $a_3=a_2+d$ The definition of the third term of an arithmetic sequence

  $a_3=a_1+d+d$ Substitute $a_2=a_1+d$

  $a_3=a_1+2d$

  $a_3=a_1+2d$

  $a_3=a_1+(3-1)d$ We know that 3 − 1 = 2

  $a_n=a_1+(n-1)·d$

Thus, $a_n=a_1+(n-1)·d$ proved