How to find the nth term in an arithmetic sequence?

Find the 53 term of the arithmetic sequence...

27, 11, −5, .......

Think about slots....

Slot 1 Slot 2 Slot 3 Slot n 27

11

-5

?

Let's write the explicit form:

an = a1 + (n − 1)d Common difference d First element a1 Term n

27, 11, −5, ....... d = a2 − a1 a1 = 27 d = 11 − 27 a2 = 11 Ready!!

an = a1 + (n − 1)d n = 53 an = 27 + (n − 1)(−16) a53 = 27 + (53 − 1)(−16) a53 = 27 + 52(−16) a53 = −805