Question

HELP PLEASE!!

Question 1 (2 points)
Generalize the pattern by finding the nth term.
6, 10, 14, 18, 22,
A. 4n
B. 4n + 2
C. 4n + 10
D. 6n + 4

Answer 1

B. 4n+2

Explanation:

You are given the pattern 6, 10, 14, 18, 22

Rewrite it as

`a_1=6\\ \\a_2=10\\ \\a_3=14\\ \\a_4=18\\ \\a_5=22`

Note that

`a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=4`

This means that given pattern is a part of arithmetic sequence with

`a_1=6\\ \\d=4`

So, the nth term of this arithmetic sequence is

`a_n=a_1+(n-1)d\\ \\a_n=6+4(n-1)\\ \\a_n=6+4n-4\\ \\a_n=4n+2`