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

Given terms and formula: We are given the first term of the sequence, a_(1)=1, and the recursive formula a_(n)=2a_(n-1)-5. To find a_(5), we need to find the values of a_(2), a_(3), a_(4), and then a_(5) using the recursive formula.Find a_(2): Let's find a_(2) using the recursive formula: a_(2) = 2a_(1) - 5 a_(2) = 2(1) - 5 a_(2) = 2 - 5 a_(2) = -3 We have found that a_(2) is -3.Find a_(3): Now let's find a_(3) using the recursive formula: a_(3) = 2a_(2) - 5 a_(3) = 2(-3) - 5 a_(3) = -6 - 5 a_(3) = -11 We have found that a_(3) is -11.Find a_(4): Next, we find a_(4) using the recursive formula: a_(4) = 2a_(3) - 5 a_(4) = 2(-11) - 5 a_(4) = -22 - 5 a_(4) = -27 We have found that a_(4) is -27.Find a_(5): Finally, we find a_(5) using the recursive formula: a_(5) = 2a_(4) - 5 a_(5) = 2(-27) - 5 a_(5) = -54 - 5 a_(5) = -59 We have found that a_(5) is -59.

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Find the roots of factored polynomials

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Q. If

a_{1}=1

and

a_{n}=2 a_{n-1}-5

then find the value of

a_{5}

\newline

Answer:

Given terms and formula: We are given the first term of the sequence, $a_{1}=1$ , and the recursive formula $a_{n}=2a_{n-1}-5$ . To find $a_{5}$ , we need to find the values of $a_{2}$ , $a_{3}$ , $a_{4}$ , and then $a_{5}$ using the recursive formula.
Find $a_{2}$ : Let's find $a_{2}$ using the recursive formula: $\newline$ $a_{2} = 2a_{1} - 5$ $\newline$ $a_{2} = 2(1) - 5$ $\newline$ $a_{2} = 2 - 5$ $\newline$ $a_{2} = -3$ $\newline$ We have found that $a_{2}$ is $-3$ .
Find $a_{3}$ : Now let's find $a_{3}$ using the recursive formula: $\newline$ $a_{3} = 2a_{2} - 5$ $\newline$ $a_{3} = 2(-3) - 5$ $\newline$ $a_{3} = -6 - 5$ $\newline$ $a_{3} = -11$ $\newline$ We have found that $a_{3}$ is $-11$ .
Find $a_{4}$ : Next, we find $a_{4}$ using the recursive formula: $\newline$ $a_{4} = 2a_{3} - 5$ $\newline$ $a_{4} = 2(-11) - 5$ $\newline$ $a_{4} = -22 - 5$ $\newline$ $a_{4} = -27$ $\newline$ We have found that $a_{4}$ is $-27$ .
Find $a_{5}$ : Finally, we find $a_{5}$ using the recursive formula: $\newline$ $a_{5} = 2a_{4} - 5$ $\newline$ $a_{5} = 2(-27) - 5$ $\newline$ $a_{5} = -54 - 5$ $\newline$ $a_{5} = -59$ $\newline$ We have found that $a_{5}$ is $-59$ .