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If the second term of an arithmetic sequence is -7 and the fifth term is 16, then what is the fourteenth term?

 

Thank you!

 Dec 13, 2020
 #1
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2nd to 6th term is 4 d

4d = 16 - -7

d = 23/4

6th term to 14th term is eight mor d's

16 + (8)(23/4)

= 16 + 46 = ........

 Dec 13, 2020
 #3
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**** edit ***

2nd to 5th term is 3 d

3d = 16 - -7

d = 23/3

5th term to 14th term is nine mor d's

16 + (9)(23/3) = 85

Sorry for the error ....I originally used 16 as the SIXTH term instead of the FIFTH term

**

Guest Dec 13, 2020
 #2
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 -7 = F + D
16 = F + 4 D, solve for F, D

 

F =-44 / 3 - this is the first term

D = 23 / 3 - this is the common difference

 

14th term = - 44/3 + (23/3 * (14 - 1))

                  = - 44/3 +  99 2/3

                  = 85 - this is the 14th term.

 Dec 13, 2020

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