Question

The simple formula for the nth term of an arithmetic sequence is an = 4n + 16. What is the explicit formula corresponding to the simple formula?

Answer 1

1 th term

a1 = 4 * 1 + 16 = 4 + 16 = 20


2 th term

a2 = 4 * 2 + 16 = 8 + 16 = 24


3 th term

a3 = 4 * 3 + 16 = 12 + 16 = 28


4 th term

a4 = 4 * 4 + 16 = 16 + 16 = 32

etc.

Arithmetic sequence with first term
a1 = 20

and common difference d = 4


General formula for arithmetic sequence :

an = a1 + ( n - 1 ) * d

In this case :

an = 20 + ( n - 1 ) * 4

Answer 2

Write the explicit formula for the geometric sequence.

a1 = -5 a2 = 20 a3 = -80