Question

Previous Which term of the arithmetic sequcnc1, 9, 17, 25, ... is 265? It is the th term. Question Help: D Video

Answer 1

265 is the 34th term

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 1 and d = a₂ - a₁ = 9 - 1 = 8 , then

`a_(n)` = 1 + 8(n - 1) = 1 + 8n - 8 = 8n - 7

now equate the nth term to 265 and solve for n

8n - 7 = 265 ( add 7 to both sides )

8n = 272 ( divide both sides by 8 )

n = 34

then 265 is the 34th term in the sequence