Question

Find the number of terms in the sequence _3 , 0, 3,____,54?​

Answer 1

n = 20

Explanation:

there is a common difference between consecutive terms , tat is

0 - (- 3) = 3 - 0 = 3

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 3 and d = 3 with
`a_(n)` = 54 , then solving for n

- 3 + 3(n - 1) = 54 ( add 3 to both sides )

3(n - 1) = 57 ( divide both sides by 3 )

n - 1 = 19 ( add 1 to both sides )

n = 20

there are 20 terms in the sequence.