Question

Given the arithmetic sequence -9,-4, 1, 4,... Which term has a value of 166?

Answer 1

jimrgrant1 made this so give him the credit, i put it here because his was reported

Answer:

36th term

Explanation:

The nth term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 9 and d = - 4 - (- 9) = - 4 + 9 = 5 , then

= - 9 + 5(n - 1) = - 9 + 5n - 5 = 5n - 14

Equate the nth term to 166 and solve for n

5n - 14 = 166 ( add 14 to both sides )

5n = 180 ( divide both sides by 5 )

n = 36

Answer 2

36th term

Explanation:

The nth 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 = - 9 and d = - 4 - (- 9) = - 4 + 9 = 5 , then

`a_(n)` = - 9 + 5(n - 1) = - 9 + 5n - 5 = 5n - 14

Equate the nth term to 166 and solve for n

5n - 14 = 166 ( add 14 to both sides )

5n = 180 ( divide both sides by 5 )

n = 36