Several terms of a sequence {an}n-1 are given below (1, -4, 16, -64, 256, ) a. F

Question

Several terms of a sequence {an}n-1 are given below (1, -4, 16, -64, 256, ) a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence). c. Find an explicit formula for the general nth term of the sequence a. The next two terms of the sequence are a6-D and a,- (Simplify your answers.) b. Choose the correct answer below. an an + 1=4-, al=1, for n21 OB, an + 1--4an , al=1,for n21 OC, an + 1-an-4,a1 = 1, for n21 OD, an-1-an +4,a1 = 1 , for n21 C. The explicit formula for the general nth term of the sequence is an- , n21.

Explanation / Answer

an=1, -4,16,-64,256......

a. Here every second term is the product of -4 and last term

So next two terms are

256*-4=-1024

-1024*-4=4096

b. Recursive formula

an+1=an*-4= -4 an

c. THe given series is in geometric progression with first term =1 and ratio=-4

So we get

an= a rn-1 = 1(-4)n-1 = (-4)n-1

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