Question

This is an arithmetic sequence. 5, 2, -1, –4, . ..
What is a7 (7th term) ?

Answer 1

⇒ to find the 7th term we should have the first term a and the common difference d

⇒The first term is 5

⇒For the difference is

`d=T_(n+1) -T_(n) \\d=2-5\\d= -3`

⇒To get the the term in an arithmetic sequence you use the formula

`T_(n)=a+(n-1)d\\`

To find the 7th term in the place of n plug in 7 and simplify the formula.

you get:

`T_(7) =a+(7-1)d\\T_(7)=a+6d`

⇒Now that we have the value of a and d let us plug in the values of a and d in place a simplify to get the value of the 7th term.

`a=5,d=-3\\T_(7)=5+6(-3)\\T_(7)=5-18\\T_(7)=-13`

⇒The 7th term is -13

Answer 2

-13

Explanation:

Nth term is 8-3n

Substitute 7 for n

8-3×7

=-13