Question

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

A. Find the 100th term when the first term is -3 and the common difference is 4.
B. Find the 7th term when the first term is -1 and the common difference is 10.
C. Find the 5th term when the first term is 7 and the common difference is -2.
D. Find the 3rd term when the first term is 2 and the common difference is 5.

Answer 1

We choose the recursive formula if we want to find the next number in a sequence. We choose the explicit formula if we want to find any number in a sequence.

So, the answer would be A because it would take a long time to find the 100th term

Answer 2

A. Find the 100th term when the first term is -3 and the common difference is 4.

Explanation:

Recursive formula for an arithmetic sequence for the nth element a(n) is
a(n) = a(n-1) + d

Thus using the recursive formula would involve computing a(n-1) which would require calculating a(n-2) and so on.

For large n such as n = 100 in case of option A this is not practical.

For smaller n's it is OK to use recursive formula

Use the explicit formula instead

a(n) = a(1) + d(n-1)