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?

A. an = 16 + (n - 1)(4)
B. an = 20 + (n - 1)(4)
C. an = 16 + 4n
D. an = 20 + (n)(4)
E. an = 4 + (n - 1)(16)

Answer 1

compare 4n + 16 with the general form for arithmetic sequence

an = a1 + (n - 1)d

an = dn + a1 - d
an = 4n + 16

Comparing coefficients:-

dn = 4n therefore d = 4

a1 - d = 16
a1 - 4 = 16
a1 = 16 + 4 = 20

therefore explicit formula is

an = 20 + (n -1)4

It's B.