Question

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

Answer 1

Answer:

$a_6_3=371$

Step-by-step 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

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

$a_6_3=-1+6(62)$

$a_6_3=-1+372$

$a_6_3=371$