Find the 8th term of the Geometric Sequence.
an=2⋅(12)n−1
really? Just plug in n=8
a8 = 2*12^(8-1) = 2*12^7
To find the 8th term of the geometric sequence given by the formula an=2⋅(12)n−1, we need to substitute n = 8 into the formula and evaluate.
Let's plug in n = 8:
a8 = 2⋅(12)8−1
Simplifying the exponent:
a8 = 2⋅(12)7
Using the power rule of exponents:
a8 = 2⋅12^7
Evaluating 12^7:
a8 = 2⋅35831808
Multiplying:
a8 ≈ 71,663,616
Therefore, the 8th term of the geometric sequence is approximately 71,663,616.
To find the 8th term of the geometric sequence, you can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1),
where an represents the nth term, a1 is the first term, r is the common ratio, and n is the position of the term.
In this case, we are given the formula for the nth term, which is:
an = 2 * (12)^(n-1).
To find the 8th term, we substitute n = 8 into the formula:
a8 = 2 * (12)^(8-1).
Simplifying the exponent:
a8 = 2 * (12)^7.
Calculating the value of (12)^7:
(12)^7 = 35831808.
Multiplying this value by 2:
a8 = 2 * 35831808.
a8 ≈ 71663616.
Therefore, the 8th term of the geometric sequence is approximately 71663616.