# Math

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In an arithmetic sequence, the first term is 5, and the fifth term is 21. What is the second term? Help please ASAP!!

• Math -

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

an = a1 + ( n - 1 ) * d

In this case:

a1 = 5

n = 5

a5 = 21

an = a1 + ( n - 1 ) * d

a5 = a1 + ( 5 - 1 ) * d

21 = 5 + 4 * d

21 - 5 = 4 d

16 = 4 d Divide both sides with 4

16 / 4 = 4 d / 4

4 = d

d = 4

a2 = a1 + d

a2 = 5 + 4

a2 = 9

• Math -

The increase per term is (21 - 5)/(5 - 1)
= 16/4 = 4

Add 4 to the first term to get the second term

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