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3. Given the recursive equation for each arithmetic sequence, write the explicit equation.

f(n)=f(n-1)-2; f(1)=8
f(n)=5+f(n-1);f(1)=0

3. Given the recursive equation for each arithmetic sequence, write the explicit equation-example-1
User Parag Doke
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1 Answer

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Given:

The recursive formulae are:

(a)
f(n)=f(n-1)-2; f(1)=8

(b)
f(n)=5+f(n-1); f(1)=0

To find:

The explicit equation.

Solution:

A recursive formula of an arithmetic sequence is


f(n)=f(n-1)+d and f(1) is the first term.

Where, d is the common difference.

The explicit formula is


f(n)=a+(n-1)d

where, a is first term and d is common difference.

(a)

We have,


f(n)=f(n-1)-2; f(1)=8

Here, first term is 8 and common difference is -2. So, the explicit formula is


f(n)=8+(n-1)(-2)


f(n)=8-2n+2


f(n)=10-2n

Therefore, the explicit formula is
f(n)=10-2n.

(b)

We have,


f(n)=5+f(n-1); f(1)=0

Here, first term is 0 and common difference is 5. So, the explicit formula is


f(n)=0+(n-1)(5)


f(n)=5n-5

Therefore, the explicit formula is
f(n)=5n-5.

User Draz
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