Answer:
24,576.
Step-by-step explanation:
We have been given that first term of a geometric sequence is 6 and common ratio is 4. We are asked to find the 7th term of the sequence.
We know that a geometric sequence is in form \(a_n=a_1\cdot r^{n-1}\), where,
\(a_n\) = nth term of sequence,
\(a_1\) = 1st term of sequence,
\(r\) = common ratio.
Upon substituting \(a_1=6\) and \(r=4\) and \(n=7\) in geometric sequence formula, we will get:
\(a_7=6\cdot(4)^{7-1}\)
\(a_7=6\cdot(4)^{6}\)
\(a_7=6\cdot 4,096\)
\(a_7=24,576\)
Therefore, the 7th term of the given geometric sequence would be 24,576.
