Question

Review

18. Find the next three terms in each sequence and write a recursive formula.
a. 42, 45, 48,...
b. 16, 40, 100,...

Answer 1

Answer:
`\bold{a)\quad 51, 54, 57\qquad a_n=a_(n-1)+3}`

`\bold{b)\quad 250, 625, 1562.5\qquad a_n=(2.5)a_(n-1)}`

Explanation:

a) This is an arithmetic sequence where 3 is added to the previous term.

48 + 3 = 51

51 + 3 = 54

54 + 3 = 57

The recursive formula for this sequence is:
`a_n = a_(n-1)+3`

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b) This is a geometric sequence where 2.5 is multiplied to the previous term.

100(2.5) = 250

250 (2.5) = 625

625(2.5) = 1562.5

The recursive formula for this sequence is:
`a_n=(2.5)a_(n-1)`