If a_(1)=9 and a_(n)=na_(n-1)-2 then find the value of a_(5). Answer:

Understand Formula and Condition: Understand the recursive formula and the initial condition. The recursive formula given is a_(n)=na_(n-1)-2, which means each term is n times the previous term minus 2. The initial condition is a_(1)=9.Find a_(2): Find the value of a_(2) using the recursive formula. Substitute n=2 and a_(1)=9 into the formula. a_(2) = 2 * a_(1) - 2 a_(2) = 2 * 9 - 2 a_(2) = 18 - 2 a_(2) = 16Find a_(3): Find the value of a_(3) using the recursive formula. Substitute n=3 and a_(2)=16 into the formula. a_(3) = 3 * a_(2) - 2 a_(3) = 3 * 16 - 2 a_(3) = 48 - 2 a_(3) = 46Find a_(4): Find the value of a_(4) using the recursive formula. Substitute n=4 and a_(3)=46 into the formula. a_(4) = 4 * a_(3) - 2 a_(4) = 4 * 46 - 2 a_(4) = 184 - 2 a_(4) = 182Find a_(5): Find the value of a_(5) using the recursive formula. Substitute n=5 and a_(4)=182 into the formula. a_(5) = 5 * a_(4) - 2 a_(5) = 5 * 182 - 2 a_(5) = 910 - 2 a_(5) = 908

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

a_{1}=9

and

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

then find the value of

a_{5}

\newline

Answer:

Understand Formula and Condition: Understand the recursive formula and the initial condition. $\newline$ The recursive formula given is $a_{n}=na_{n-1}-2$ , which means each term is $n$ times the previous term minus $2$ . The initial condition is $a_{1}=9$ .
Find $a_{2}$ : Find the value of $a_{2}$ using the recursive formula. $\newline$ Substitute $n=2$ and $a_{1}=9$ into the formula. $\newline$ $a_{2} = 2 \times a_{1} - 2$ $\newline$ $a_{2} = 2 \times 9 - 2$ $\newline$ $a_{2} = 18 - 2$ $\newline$ $a_{2} = 16$
Find $a_{3}$ : Find the value of $a_{3}$ using the recursive formula. $\newline$ Substitute $n=3$ and $a_{2}=16$ into the formula. $\newline$ $a_{3} = 3 \times a_{2} - 2$ $\newline$ $a_{3} = 3 \times 16 - 2$ $\newline$ $a_{3} = 48 - 2$ $\newline$ $a_{3} = 46$
Find $a_{4}$ : Find the value of $a_{4}$ using the recursive formula. $\newline$ Substitute $n=4$ and $a_{3}=46$ into the formula. $\newline$ $a_{4} = 4 \times a_{3} - 2$ $\newline$ $a_{4} = 4 \times 46 - 2$ $\newline$ $a_{4} = 184 - 2$ $\newline$ $a_{4} = 182$
Find $a_{5}$ : Find the value of $a_{5}$ using the recursive formula. $\newline$ Substitute $n=5$ and $a_{4}=182$ into the formula. $\newline$ $a_{5} = 5 \times a_{4} - 2$ $\newline$ $a_{5} = 5 \times 182 - 2$ $\newline$ $a_{5} = 910 - 2$ $\newline$ $a_{5} = 908$