If a_(1)=5 and a_(n)=-2a_(n-1)+1 then find the value of a_(4). Answer:

Identify first term: Identify the first term in the sequence. We are given that a_(1) = 5, which is the first term of the sequence.Find second term: Use the recursive formula to find the second term, a_(2). The recursive formula is a_(n) = -2a_(n-1) + 1. Substitute n = 2 to find a_(2). a_(2) = -2a_(1) + 1 = -2(5) + 1 = -10 + 1 = -9.Find third term: Use the recursive formula to find the third term, a_(3). Substitute n = 3 to find a_(3). a_(3) = -2a_(2) + 1 = -2(-9) + 1 = 18 + 1 = 19.Find fourth term: Use the recursive formula to find the fourth term, a_(4). Substitute n = 4 to find a_(4). a_(4) = -2a_(3) + 1 = -2(19) + 1 = -38 + 1 = -37.

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If
a_(1)=5 and
a_(n)=-2a_(n-1)+1 then find the value of
a_(4).
Answer:

If $a_{1}=5$ and $a_{n}=-2 a_{n-1}+1$ then find the value of $a_{4}$ . $\newline$ Answer:

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

a_{1}=5

and

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

then find the value of

a_{4}

\newline

Answer:

Identify first term: Identify the first term in the sequence. $\newline$ We are given that $a_{1} = 5$ , which is the first term of the sequence.
Find second term: Use the recursive formula to find the second term, $a_{2}$ . The recursive formula is $a_{n} = -2a_{n-1} + 1$ . Substitute $n = 2$ to find $a_{2}$ . $a_{2} = -2a_{1} + 1 = -2(5) + 1 = -10 + 1 = -9$ .
Find third term: Use the recursive formula to find the third term, $a_{3}$ . Substitute $n = 3$ to find $a_{3}$ . $a_{3} = -2a_{2} + 1 = -2(-9) + 1 = 18 + 1 = 19$ .
Find fourth term: Use the recursive formula to find the fourth term, $a_{4}$ . Substitute $n = 4$ to find $a_{4}$ . $a_{4} = -2a_{3} + 1 = -2(19) + 1 = -38 + 1 = -37$ .