Question

Find the indicated term of the arithmetic sequence.


22nd term: a1 = 4; d = 4

Answer 1

88

Explanation:

airthmetic sequences are linear.

This means no matter what two points you choose from an arithmetic sequence the slope (the common difference,d) will be constant.

`(a_(22)-a_1)/(22-1)=d`

`(a_(22)-4)/(22-1)=4`

`(a_(22)-4)/(21)=4`

Multiply both sides by 21:

`a_(22)-4=21(4)`

`a_(22)-4=84`

Add 4 on both sides:

`a_(22)=88`

The 22nd term is 88.

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Or the explicit form for an arithmetic sequence is:

`a_n=a_1+d(n-1)`

`a_n=4+4(n-1)`

We want to know the 22nd term which means we need to replace n with 22:

`a_(22)=4+4(22-1)`

`a_(22)=4+4(21)`

`a_(22)=4+84`

`a_(22)=88`