Question

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Find the 5th term for the following recursive formulas/sequences. SHOW YOUR WORK!!

c. 1/6, 2/3, 8/3, . . .

Answer 1

128/3

Explanation:

The sequence follow the rule (1/6)*(4)^(n-1). The 5th term will be (1/6)*(4)^4=128/3

Answer 2

128/3

Explanation:

1/6, 2/3, 8/3, . . .

1/6, 4/6, 16/6

We are multiplying by 4 each time

1/6 *4 = 4/6

4/6 * 4 = 16/6

This is a geometric sequence with the common ratio of 4

an = a1 (r)^(n-1)

an = 1/6 (4) ^(n-1)

Let n = 5

a5 = 1/6 (4)^(5-1)

a5 = 1/6 (4)^4

a5 = 1/6 * 256

a5 =128/3