# 8,a,14,b,20Which of these could be the formula for any postive interger n?A.2n+ 6 B.3n+5 C.5n+3 D.6n+2 E.6n+5Y

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In order to get from one term to the next, you add 3.

8+3 is 11, 11+3 is 14, 14+3 is 17, 17 + 3 is 20. Since you add 3 between terms, the *common difference* is 3, and that is the number *multiplied by n*.

So, now you have 3n + ____. To fill in the blank, use the first term, when n = 1. To have 3(1) + ____ = 8, the blank must be 5, so the correct answer is 3n + 5. B

b . 3n + 5

if you plug in with numbers you will get the sequence shown above

It is B( 3n+5)

If you sub n=1, the answer is 8

sub n=2 and the answer (a) is 11

sub n=3 and answer is 14

sub n=4 and answer (b) is 17

sub n=5 and answer is 20

Thus, this general term fits the pattern, and also solves for a and b.

3n + 5

if the seuence is 8,a,14,b,20

if you plug in 1=n to the formula then you get 8

if you plug in 2=n to the formula then you get 11

if you plug in 3=n to the formula then you get 14

if you plug in 4=n to the formula then you get 17

if you plug in 5=n to the formula then you get 20

so it fits the pattern you can keep it going if you needed to.