MATH SOLVE

1 month ago

Q:
# -3,6,-9,12,-15 which of the following represents the general term for the sequence give? (-1)^n3^n(-1)^n3n(-1)^n+1(3)

Accepted Solution

A:

The general term for the sequence [tex]a_{n}=(-1)^{n} 3 n[/tex]Solution:Given sequence is -3, 6, -9, 12, -15We have to find the general term of sequenceThe terms in the sequence are found out by using the recursive definition:[tex]a_{n}=(-1)^{n} 3 n[/tex]Let us use this definition to find out the terms and check if it matches our given sequence[tex]\begin{array}{l}{\text { For } n=1:-(-1)^{n} 3 n=(-1)^{1} \times 3 \times 1=-3} \\\\ {\text { For } n=2:-(-1)^{n} 3 n=(-1)^{2} \times 3 \times 2=1 \times 6=6} \\\\ {\text { For } n=3:-(-1)^{n} 3 n=(-1)^{3} \times 3 \times 3=-1 \times 9=-9} \\\\ {\text { For } n=4:-(-1)^{n} 3 n=(-1)^{4} \times 3 \times 4=1 \times 12=12} \\\\ {\text { For } n=5:-(-1)^{n} 3 n=(-1)^{5} \times 3 \times 5=-1 \times 15=-15}\end{array}[/tex]Thus the general term is given by [tex]a_{n}=(-1)^{n} 3 n[/tex]