In which situation below would you want to use the Explicit Formula instead of the Recursive Formula?

A. Find the 4th term when the first term is 7 and the common difference is -2.
B.Find the 7th term when the first term is -1 and the common difference is 10.
C.Find the 106th term when the first term is 2 and the common difference is 5.
D.Find the 11th term when the first term is -3 and the common difference is 4.

The recursive formula is good if you have terms near the one of interest. It might be used for the 4th term, but that would require that you compute the three previous terms:

7, 5, 3, 1 . . . . requires 3 subtractions

It can be about as easy to calculate ...

a4 = 7 -2(3) = 1 . . . . requires two* subtractions and a multiplication

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However, for the 7th, 11th, and 106th terms, it is impractical to list all previous terms. The explicit formula is a better choice.

A. a4 = 7 -2(3) = 1

B. a7 = -1 +10(6) = 59

C. a106 = 2 +5(105) = 527

D. a11 = -3 +4(10) = 37

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* The explicit formula is ...

an = a1 +d(n -1)

The operations identified in this formula (in the order required by the Order of Operations) are subtraction, multiplication, and addition. For a negative common difference, that amounts to two subtractions and a multiplication.

For manual evaluation, the work involved in using the recursive or explicit formulas for the 4th term is about the same, if the arithmetic is easily done mentally (as here).