To determine the 20th term of the sequence \(-3, 6, -12, 24, \ldots\), we need to identify the pattern of the sequence. Let's examine the first few terms and find a relationship between them.
The given sequence is:
- First term (\(a_1\)) = \(-3\)
- Second term (\(a_2\)) = \(6\)
- Third term (\(a_3\)) = \(-12\)
- Fourth term (\(a_4\)) = \(24\)
Notice the pattern in which the terms are changing:
\[
a_2 = -2 \times a_1 = -2 \times (-3) = 6
\]
\[
a_3 = -2 \times a_2 = -2 \times 6 = -12
\]
\[
a_4 = -2 \times a_3 = -2 \times (-12) = 24
\]
It appears that each term is obtained by multiplying the previous term by \(-2\). Hence, this is a geometric sequence with the first term \(a_1 = -3\) and a common ratio \(r = -2\).
The \(n\)-th term of a geometric sequence can be found using the formula:
\[
a_n = a_1 \times r^{(n-1)}
\]
We need to find the 20th term (\(a_{20}\)):
\[
a_{20} = -3 \times (-2)^{19}
\]
Calculate \((-2)^{19}\):
Since \(19\) is an odd number, \((-2)^{19}\) will be negative and:
\[
(-2)^{19} = -524288
\]
Now, multiply this by \(-3\):
\[
a_{20} = -3 \times -524288 = 1572864
\]
Therefore, the 20th term of the sequence is:
\[
1572864
\]
What is the 20th term of the sequence that begins -3,6,-12,24?
1 answer
1 answer