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3 years ago

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An arithmetic sequence has this recursive formula: A1=5 An=an-1-4

1 answer:

Olenka [21]3 years ago

8 0

Answer:

A recursive formula designates the starting term, a1, and the nth term of the sequence, an , as an expression containing the previous term (the term before it), an-1.Find a recursive formula. This example is an arithmetic sequence (the same number, 5, is added to each term to get to the next term).

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What are the first three terms of the sequence modeled by the recursive function an=1/2an-1 when a1=1?

loris [4]

Answer:

Option A is correct that is $1,\frac{1}{2},\frac{1}{4}$

Step-by-step explanation:

We have been given a formula $a_n=\frac{1}{2}\cdot a_n-1$

$a_1=1$

We will put values of n in $a_n=\frac{1}{2}\cdot a_n-1$

when n=2 we get

$a_2=\frac{1}{2}\cdot a_2-1$

$\Rightarrow a_2=\frac{1}{2}\cdot a_1$

$\Rightarrow a_2=\frac{1}{2}\cdot 1$

$\Rightarrow a_2=\frac{1}{2}$

when n=3

$a_3=\frac{1}{2}\cdot a_2$

$\Rightarrow a_3=\frac{1}{2}\cdot \frac{1}{2}$

$\Rightarrow a_3=\frac{1}{4}$

Therefore, Option A is correct that is $1,\frac{1}{2},\frac{1}{4}$

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Bond [772]

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