Question

Find a formula for the n th term, T n , of the following arithmetic sequence: 13 , 17 , 21 , 25 , . . . Hence, or otherwise, find the value of the 40th term, T 40 .

Answer 1

tₙ = 4n + 9

t₄₀ = 169

Explanation:

17-13=4 and 21-17=4 and 25-21=4 so d=4

`t_n=t_1+d(n-1)\\\\t_1=13\\d=4\\\\t_n=13+4(n-1)\\\\t_n=13+4n-4\\\\\underline{t_n=4n+9}`

`t_(40)=4\cdot40+9=160+9=169`