Question

Write an Explicit formula for a1 = –2, an = an – 1 + 4, n ≥ 2

A. an = –4n – 6
B. an = –2n – 6
C. an = 4n – 6
D. an = 4n + 6

Answer 1

According to the recursive formula,

`a_2=a_1+4`

`a_3=a_2+4=(a_1+4)+4=a_1+2\cdot4`

`a_4=a_3+4=a_2+2\cdot4=a_1+3\cdot4`

and so on, with the general formula

`a_n=a_1+(n-1)\cdot4`

Then

`a_n=-2+4(n-1)=4n-6`

and the answer is C.

Answer 2

C. an = 4n -6

Explanation:

Only one of the offered choices gives a1=-2 for n=1.

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The recursive formula tells you ...

a2 -a1 = 4

The only choices that increase by 4 when n increases by 1 are choices C and D. Of these, choice D gives a1=4·1+6 = 10 ≠ -2.

Choice C gives a1 = 4·1 -6 = -2, as required.