Question

Find the number of terms in the arithmetic progression 2,-9,-20,...,-141​

Answer 1

`14`

Explanation:

The nth term of this sequence is:

`-11n+13`

Solve the equation for n.

`-11n+13=-141`

`-11n=-141-13`

`-11n=-154`

`11n=154`

`n=154 / 11`

`n=14`

Answer 2

14

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

Here a₁ = 2 , d = - 9 - 2 = - 11 and
`a_(n)` = - 141, thus

2 - 11(n - 1) = - 141 ← distribute and simplify left side

2 - 11n + 11 = - 141

13 - 11n = - 141 ( subtract 13 from both sides )

- 11n = - 154 ( divide both sides by - 11 )

n = 14

That is the progression has 14 terms