If a_(1)=3,a_(2)=5 and a_(n)=2a_(n-1)+2a_(n-2) then find the value of a_(5). Answer:

Calculate a_(3): To find a_(5), we need to use the recursive formula a_(n)=2a_(n-1)+2a_(n-2) to find a_(3) and a_(4) first.Calculate a_(4): Using the recursive formula, let's calculate a_(3): a_(3) = 2a_(2) + 2a_(1) = 2*5 + 2*3 = 10 + 6 = 16.Find a_(5): Now, let's calculate a_(4) using the recursive formula: a_(4) = 2a_(3) + 2a_(2) = 2*16 + 2*5 = 32 + 10 = 42.Finally, we can find a_(5) using the values of a_(3) and a_(4): a_(5) = 2a_(4) + 2a_(3) = 2*42 + 2*16 = 84 + 32 = 116.

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Precalculus

Find the roots of factored polynomials

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Q. If

a_{1}=3, a_{2}=5

and

a_{n}=2 a_{n-1}+2 a_{n-2}

then find the value of

a_{5}

\newline

Answer:

Calculate $a_{3}$ : To find $a_{5}$ , we need to use the recursive formula $a_{n}=2a_{n-1}+2a_{n-2}$ to find $a_{3}$ and $a_{4}$ first.
Calculate $a_{4}$ : Using the recursive formula, let's calculate $a_{3}$ : $\newline$ $a_{$3$} = $2$a_{$2$} + $2$a_{$1$} = $2$\times $5$ + $2$\times $3$ = $10$ + $6$ = $16$.
Find $a_{5}$: Now, let's calculate $a_{4}$ using the recursive formula:$\newline$$a_{4} = 2a_{3} + 2a_{2} = 2\times16 + 2\times5 = 32 + 10 = 42$.
Find $a_{5}$: Now, let's calculate $a_{4}$ using the recursive formula:$\newline$$a_{4} = 2a_{3} + 2a_{2} = 2\times16 + 2\times5 = 32 + 10 = 42$.Finally, we can find $a_{5}$ using the values of $a_{3}$ and $a_{4}$:$\newline$$a_{5} = 2a_{4} + 2a_{3} = 2\times42 + 2\times16 = 84 + 32 = 116$.