Question

Write a rule for the nth term of the arithmetic sequence. d =1/2 , a6 =18.

Answer 1

Answer:

$a_{n}$ = $\frac{1}{2}$ n + 15

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

Given a₆ = 18 and d = $\frac{1}{2}$ , then

a₁ + 5d = 18 , that is

a₁ + $\frac{5}{2}$ = 18 ( subtract $\frac{5}{2}$ from both sides )

a₁ = $\frac{31}{2}$

Thus

$a_{n}$ = $\frac{31}{2}$ + $\frac{1}{2}$ (n - 1) = $\frac{15}{2}$ + $\frac{1}{2}$ n - $\frac{1}{2}$ = $\frac{1}{2}$ n + 15