Which recursive sequence would produce the sequence 5,-11,37,dots ? a_(1)=5 and a_(n)=-a_(n-1)-2 a_(1)=5 and a_(n)=-3a_(n-1)+4 a_(1)=5 and a_(n)=-2a_(n-1)-1 a_(1)=5 and a_(n)=4a_(n-1)-3

Identify first term: Identify the first term of the sequence. The first term given is a_(1) = 5.Calculate second term: Calculate the second term using each recursive formula and compare with the given second term (-11). a) Using the first formula: a_(n) = -a_(n-1) - 2 a_(2) = -a_(1) - 2 = -5 - 2 = -7 This does not match the given second term (-11).Calculate third term: b) Using the second formula: a_(n) = -3a_(n-1) + 4 a_(2) = -3a_(1) + 4 = -3*5 + 4 = -15 + 4 = -11 This matches the given second term (-11).Verify correct formula: Calculate the third term using the second formula to verify if it matches the given third term (37). a_(3) = -3a_(2) + 4 = -3*(-11) + 4 = 33 + 4 = 37 This matches the given third term (37).Since the second formula correctly produces the first three terms of the sequence, we conclude that it is the correct recursive formula. The correct recursive sequence formula is: a_(1) = 5 and a_(n) = -3a_(n-1) + 4

Home

Math Problems

Algebra 1

Identify a sequence as explicit or recursive

Full solution

Q. Which recursive sequence would produce the sequence

5,-11,37, \ldots

\newline

a_{1}=5

and

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

\newline

a_{1}=5

and

a_{n}=-3 a_{n-1}+4

\newline

a_{1}=5

and

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

\newline

a_{1}=5

and

a_{n}=4 a_{n-1}-3

Identify first term: Identify the first term of the sequence. $\newline$ The first term given is $a_{1} = 5$ .
Calculate second term: Calculate the second term using each recursive formula and compare with the given second term $-11$ . $\newline$ a) Using the first formula: $a_{n} = -a_{n-1} - 2$ $\newline$ $a_{2} = -a_{1} - 2 = -5 - 2 = -7$ $\newline$ This does not match the given second term $-11$ .
Calculate third term: b) Using the second formula: $a_{n} = -3a_{n-1} + 4$ $\newline$ $a_{2} = -3a_{1} + 4 = -3\times 5 + 4 = -15 + 4 = -11$ $\newline$ This matches the given second term ( $-11$ ).
Verify correct formula: Calculate the third term using the second formula to verify if it matches the given third term $37$ . $a_{3} = -3a_{2} + 4 = -3*(-11) + 4 = 33 + 4 = 37$ This matches the given third term $37$ .
Verify correct formula: Calculate the third term using the second formula to verify if it matches the given third term $37$ . $a_{3} = -3a_{2} + 4 = -3*(-11) + 4 = 33 + 4 = 37$ This matches the given third term $37$ .Since the second formula correctly produces the first three terms of the sequence, we conclude that it is the correct recursive formula. The correct recursive sequence formula is: $a_{1} = 5$ and $a_{n} = -3a_{n-1} + 4$