Question

Find the number of terms in the sequence or the sum of the sequence as requested. Find the number of terms in the following arithmetic sequence. 3,9,15,21,…,81 11

8
17
14

Answer 1

14 terms

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + d(n - 1)

a₁ is the first term and d the common difference

here a₁ = 3 and d = a₂ - a₁ = 9 - 3 = 6

substitute these values into the nth term formula

`a_(n)` = 3 + 6(n - 1) = 3 + 6n - 6 = 6n - 3

TO find the number of terms (n) equate
`a_(n)` to81 and solve for n

6n - 3 = 81 ( add 3 to both sides )

6n = 84 ( divide both sides by 6 )

n = 14

There are 14 terms in the sequence