Question

A7=26 a16=71 write a rule for the nth term

Answer 1

`a_(n)` = 5n - 9

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

a₁ and d have to be found to obtain the nth term rule

given a₇ = 26 and a₁₆ = 71 , then

a₁ + 6d = 26 → (1)

a₁ + 15d = 71 → (2)

subtract (1) from (2) term by term to eliminate a₁

(a₁ - a₁) + (15d - 6d) = 71 - 26

0 + 9d = 45

9d = 45 ( divide both sides by 9 )

d = 5

substitute d = 5 into (1) and solve for a₁

a₁ + 6(5) = 26

a₁ + 30 = 26 ( subtract 30 from both sides )

a₁ = - 4

then nth term rule is

`a_(n)` = - 4 + 5(n - 1) = - 4 + 5n - 5 = 5n - 9