Question

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

Answer 1

Answer:

$14$

Step-by-step explanation:

The nth term of this sequence is:

$-11n+13$

Solve the equation for n.

$-11n+13=-141$

$-11n=-141-13$

$-11n=-154$

$11n=154$

$n=154 \div 11$

$n=14$

Answer 2

Answer:

14

Step-by-step 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