To solve for the 7th term of a geometric sequence with t1 = 6 and r = 4, we use the following equation:
a(n) = a(1) r^(n-1)
a7 = (6) 4^(7-1)
a7 = 24576
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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 [tex]a_n=a_1\cdot r^{n-1}[/tex], where,
[tex]a_n[/tex] = nth term of sequence,
[tex]a_1[/tex] = 1st term of sequence,
[tex]r[/tex] = common ratio.
Upon substituting [tex]a_1=6[/tex] and [tex]r=4[/tex] and [tex]n=7[/tex] in geometric sequence formula, we will get:
[tex]a_7=6\cdot(4)^{7-1}[/tex]
[tex]a_7=6\cdot(4)^{6}[/tex]
[tex]a_7=6\cdot 4,096[/tex]
[tex]a_7=24,576[/tex]
Therefore, the 7th term of the given geometric sequence would be 24,576.
