Question

Find the 63rd term of the arithmetic sequence -1, 5, 11, ...−1,5,11,...

Answer 1

Explanation:

Answer 2

`a_6_3=371`

Explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant and this constant is called the common difference

we have

`-1,5,11,...`

Let

`a_1=-1\\a_2=5\\a_3=11`

`a_2-a_1=5-(-1)=5+1=6`

`a_3-a_2=11-5=6`

The common difference is
`d=6`

We can write an Arithmetic Sequence as a rule

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

where

a_n is the nth term

d is the common difference

a_1 is the first term

n is the number of terms

Find the 63rd term of the arithmetic sequence

we have

`n=63\\d=6\\a_1=-1`

substitute

`a_6_3=-1+6(63-1)`

`a_6_3=-1+6(62)`

`a_6_3=-1+372`

`a_6_3=371`