If a_(1)=7 and a_(n)=na_(n-1)+5 then find the value of a_(4). Answer:

Given terms and formula: We are given the first term of the sequence, a_(1) = 7, and the recursive formula for the sequence, a_(n) = n*a_(n-1) + 5. To find a_(4), we need to find the values of a_(2), a_(3), and then a_(4) using the recursive formula.Find a_(2): First, let's find a_(2) using the recursive formula. We substitute n = 2 and a_(1) = 7 into the formula: a_(2) = 2*a_(1) + 5 = 2*7 + 5 = 14 + 5 = 19.Find a_(3): Next, we find a_(3) using the recursive formula. We substitute n = 3 and a_(2) = 19 into the formula: a_(3) = 3*a_(2) + 5 = 3*19 + 5 = 57 + 5 = 62.Find a_(4): Finally, we find a_(4) using the recursive formula. We substitute n = 4 and a_(3) = 62 into the formula: a_(4) = 4*a_(3) + 5 = 4*62 + 5 = 248 + 5 = 253.

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Find the roots of factored polynomials

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Q. If

a_{1}=7

and

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

then find the value of

a_{4}

\newline

Answer:

Given terms and formula: We are given the first term of the sequence, $a_{1} = 7$ , and the recursive formula for the sequence, $a_{n} = n \cdot a_{n-1} + 5$ . To find $a_{4}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula.
Find $a_{2}$ : First, let's find $a_{2}$ using the recursive formula. We substitute $n = 2$ and $a_{1} = 7$ into the formula: $\newline$ $a_{2} = 2\cdot a_{1} + 5 = 2\cdot 7 + 5 = 14 + 5 = 19$ .
Find $a_{3}$ : Next, we find $a_{3}$ using the recursive formula. We substitute $n = 3$ and $a_{2} = 19$ into the formula: $\newline$ $a_{3} = 3\cdot a_{2} + 5 = 3\cdot 19 + 5 = 57 + 5 = 62$ .
Find $a_{4}$ : Finally, we find $a_{4}$ using the recursive formula. We substitute $n = 4$ and $a_{3} = 62$ into the formula: $\newline$ $a_{4} = 4\cdot a_{3} + 5 = 4\cdot 62 + 5 = 248 + 5 = 253$ .