Find an equation for the nth term of the arithmetic sequence. a19 = -58, a21 = -164

a. an = 896 - 53(n - 2)
b. an = 896 - 53(n - 1)
c. an = 896 + 53(n + 1)
d. an = 896 - 53(n + 1)

The common difference would be calculated as:

(a21-a19)/2

(-164--(-58 ))/2 (Replacing the values )

(-164 +58)/2 (Changing signs)

(-106)/2(Subtracting)

-53

Then we are going to replace the common difference(d) in the sequence formal with the 21st term . It is done for finding the first term of the sequence.

a21=a0+d*(n-1)

-164=a0+-53*(21-1) (Replacing the values)

-164=a1-53(20) (Subtracting)

-164=a1-1060 (Multiplying )

-164+1060=a1 (Adding 1060 on both sides of the equation)

896=a1

The answer would be : an= 896-53*(n-1), which is the option B.

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