Question

How many terms are in the arithmetic sequence 7, 1, −5, …, −161?

Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference

27
28
29
30

Answer 1

29

Explanation:

The n th term of an arithmetic sequence is

•
`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = 1 - 7 = - 5 - 1 = - 6 and a₁ = 7,
`a_(n)` = - 161, hence

7 - 6(n - 1) = - 161 ← solve for n

7 - 6n + 6 = - 161

13 - 6n = - 161 ( subtract 13 from both sides )

- 6n = - 174 ( divide both sides by - 6 )

n = 29

There are 29 terms in the sequence