Question

Find the next term is in the explicit and recursive rule for the in term of the sequence. NO LINKS!!!

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Answer 1

9514 1404 393

Answer:

5) 729, an=3^n, a[1]=3; a[n]=3·a[n-1]

6) 1792, an=7(4^(n-1)), a[1]=7; a[n]=4·a[n-1]

Explanation:

The next term of a geometric sequence is the last term multiplied by the common ratio. (This is the basis of the recursive formula.)

The Explicit Rule is ...

`a_n=a_1\cdot r^(n-1)`

for first term a₁ and common ratio r.

The Recursive Rule is ...

a[1] = a₁

a[n] = r·a[n-1]

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5. First term is a₁ = 3; common ratio is r = 9/3 = 3.

Next term: 243×3 = 729

Explicit rule: an = 3·3^(n-1) = 3^n

Recursive rule: a[1] = 3; a[n] = 3·a[n-1]

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6. First term is a₁ = 7; common ratio is r = 28/7 = 4.

Next term: 448×4 = 1792

Explicit rule: an = 7·4^(n-1)

Recursive rule: a[1] = 7; a[n] = 4·a[n-1]