Question

Write a recursive and an explicit formula to represent the following sequence 52, 40, 28, 16,...

Answer 1

Explicit tn = 52 + (n - 1)*(-12)

Recursive = tn = t(n - 1) - 12

Explanation:

The difference between term n and term n - 1 is can be found by taking the difference between and 2 consecutive terms.

t3 = 28

t2 = 40

d = t3 - t2

d = 28 - 40

d = - 12

Explicit

tn = a1 + (n - 1)*d

a1 = 52

d = - 12

tn = 52 + (n - 1)*(-12)

Example

Find t5

t5 = 52 + (5 - 1)*(-12)

t5 = 52 + 4 * - 12

t5 = 52 - 48

t5 = 4

Recursive

tn = t(n - 1) - 12

Example

t5 = t4 - 12

t5 = 16 - 12

t5 = 4 just as it did before.