In An Arithmetic Sequence 13,9,5,1, What Term Is -159?

In an arithmetic sequence 13,9,5,1, what term is -159?

 

ANSWER :

The term is 44.

STEP BY STEP EXPLANATION :

An = A1 + (n - 1) × R

-159 = 13 + (n - 1) × (9 - 13)

-159 = 13 + (n - 1) × (-4)

-159 = 13 + (-4n) + 4

-159 = (-4n) + 4 + 13

-159 = (-4n) + 17

-4n + 17 = -159

-4n = -159 - 17

-4n = -176

n = (-176)/(-4)

n = 44

  • Testing...

An = A1 + (n - 1) × R

A44 = 13 + (44 - 1) × (9 - 13)

A44 = 13 + 43 × (-4)

A44 = 13 + (-172)

A44 = 13 - 172

A44 = -159

Therefore , the term is 44.

OK.


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