If a_(1)=3 and a_(n+1)=-5a_(n)-3 then find the value of a_(4). Answer:

Given terms: We are given the first term of the sequence, a_(1)=3, and the recursive formula for the sequence, a_(n+1)=-5a_(n)-3. To find a_(4), we need to find a_(2), a_(3), and then a_(4) using the recursive formula.Find a_(2): Let's find a_(2) using the recursive formula. We substitute n=1 into the formula to get a_(2)=-5a_(1)-3. a_(2) = -5 * a_(1) - 3 a_(2) = -5 * 3 - 3 a_(2) = -15 - 3 a_(2) = -18Find a_(3): Next, we find a_(3) using the recursive formula. We substitute n=2 into the formula to get a_(3)=-5a_(2)-3. a_(3) = -5 * a_(2) - 3 a_(3) = -5 * (-18) - 3 a_(3) = 90 - 3 a_(3) = 87Find a_(4): Finally, we find a_(4) using the recursive formula. We substitute n=3 into the formula to get a_(4)=-5a_(3)-3. a_(4) = -5 * a_(3) - 3 a_(4) = -5 * 87 - 3 a_(4) = -435 - 3 a_(4) = -438

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=3

and

a_{n+1}=-5 a_{n}-3

then find the value of

a_{4}

\newline

Answer:

Given terms: We are given the first term of the sequence, $a_{1}=3$ , and the recursive formula for the sequence, $a_{n+1}=-5a_{n}-3$ . To find $a_{4}$ , we need to find $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula.
Find $a_{2}$ : Let's find $a_{2}$ using the recursive formula. We substitute $n=1$ into the formula to get $a_{2}=-5a_{1}-3$ . $\newline$ $a_{2} = -5 \times a_{1} - 3$ $\newline$ $a_{2} = -5 \times 3 - 3$ $\newline$ $a_{2} = -15 - 3$ $\newline$ $a_{2} = -18$
Find $a_{3}$ : Next, we find $a_{3}$ using the recursive formula. We substitute $n=2$ into the formula to get $a_{3}=-5a_{2}-3$ . $\newline$ $a_{3} = -5 \times a_{2} - 3$ $\newline$ $a_{3} = -5 \times (-18) - 3$ $\newline$ $a_{3} = 90 - 3$ $\newline$ $a_{3} = 87$
Find $a_{4}$ : Finally, we find $a_{4}$ using the recursive formula. We substitute $n=3$ into the formula to get $a_{4}=-5a_{3}-3$ . $\newline$ $a_{4} = -5 \times a_{3} - 3$ $\newline$ $a_{4} = -5 \times 87 - 3$ $\newline$ $a_{4} = -435 - 3$ $\newline$ $a_{4} = -438$