For each explicitly-defined sequence below, write the first few terms. Then use the terms to write a recursive equation. a. t(n) = 2n + 5

b. t(n) = 3(1/2)^n

Step-by-step explanation:

Problem A

t(1) = 2(1) + 5

t(2) = 2*2 + 5 = 9

t(3) = 2*3 + 5 = 11

t(4) = 2*4 + 5 = 13

So this is the explicit result. Now try it recursively.

t_3 = t_2 + 2

t_3 = 9 + 2

t_3 = 11          which is just what it should do.

t_n = t_(n - 1) + 2

Problem B

t(1) = 3 * 1/2

t(1) = 3/2

t(2) = 3*(1/2)^2

t(2) = 3 * 1/4

t(2) = 3/4

t(3) = 3*(1/2)^3

t(3) = 3 * 1/8

t(3) = 3/8

t(4) = 3 (1/2)^4

t(4) = 3 (1/16)

t(4) = 3/16

So in general

t_n = t_n-1 * 1/2

For example t(5)

t_5 = t_4 * 1/2

t_5 = 3 /16 * 1/2 = 3/32

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step-by-step explanation: