Question

What is the 83rd term for the arithmetic sequence

Answer 1

306

Explanation:

We know that the formula of an arithmetic sequence with the same common difference is given by:

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

where
`a_n` is the term that we want to find out,

`a_1` is the first term of the sequence,

`n` is the number or position of the unknown term; and

`d` is the common difference.

Here,
`a=-22` and
`d=-18-(-22)=4`.

So putting in these values in the formula to get:

`a_83=(-22)+(83-1)(4)`

`a_83=-22+328`

`a_83=306`

Therefore, the 83rd term of the given sequence is 306.

Answer 2

306

Explanation:

given an Arithmetic sequence with I term

a = -22, and common difference d = -18-(-22) = 4

We have to find the nth term

We know that an arithmetic sequence is a sequence which follows a pattern of adding the same d to the previous term to get the successive term.

Hence we get

`a_(n) =a+(n-1)d\\a_(83) =-22+(83-1)4 \\= -22+328\\= 306`

Thus we get 83rd term = 306