Question

The sixth term is 22 and the common difference is 6. What is the fifteenth term?

Answer 1

$T_n = a_1+ d(n-1)$

Given that d = 6 and 6th term is 22,
$22 = a_1+ 6(6-1)$
$22 = a_1+ 30$
$a_1 = 22- 30$
$a_1 = -8$

So the general equation is 
$T_n = -8 + 6(n-1)$
$T_n = -8 + 6n-6$
$T_n =6n-14$

When n = 15,
$T_{15} = 6(15)-14$
$T_{15} = 136$

Answer: 136