Several terms of a sequence fa1 are given below. 6\' 36\' 216\' 1,296 a. Find th

Question

Several terms of a sequence fa1 are given below. 6' 36' 216' 1,296 a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence. c. Find an explicit formula for the general nth term of the sequence. a. Find the next two terms of the sequence. ae* , a,- (Simplify your answers.) b. Find a recurrence relation that generates the sequence. an + 1 =Da,-, for n = 1, 2, 3,.. c. Find an explicit formula for the general nth term of the sequence. an =-, for n-1,2, 3,

Explanation / Answer

1, 1/6,1/36, 1/216,....

1/1/6,1/62,1/63,1/64

So the next two terms are 1/65=1/7776

And 1/66=1/46656

b. Here the next term is 1/6 times of the previous term

Therefore

an+1=(1/6)an

And a1=1

Here the denominators are1, 6,62,63,64,....

Which is geometric progression

With first term, a=1 and common ratio, r=6

Therefore an=a rn-1

an=1 (6)n-1

So the explicit formula is

an=1/(6)n-1

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