Question

Consider the following sequence:

7, 11, 15, 19, 23, . . .
The common difference is ______
What is the Explicit equation for the sequence?
t(n) = ____n + ______

What is the 20th term?

Answer 1

Common difference= 4, Equation; t(n)=4n+3, 20th= 83

Explanation:

d=11-7=4

Equation

Recall, t(n)=a_1+(n-1)d

Replacing a_1 =7 and d=4

t(n)=7+(n-1)4

t(n)=7+4n-4

t(n)=4n+3

20th item

t(20)=4(20)+3=83

I hope that is helpful

Answer 2

Explanation:

This is an arithmetic progression.

It starts at 7 and keeps on adding 4.

The common difference is 4

The explicit equation is

t_n = a + (n - 1)*d

a = 7

d = 4

t_n = 7 + (n - 1)*4

t_n = 7 + 4n - 4

t_n = 4n + 3

t_20

t_20 = 4*20 + 3

t_20 = 83