Find the 13th term of the geometric sequence 7,-35,175,...
To find the 13th term of a geometric sequence, we first need to determine the common ratio (r) of the sequence. The common ratio can be found by dividing any term by the previous term.
In this case,
r = -35/7
r = -5
Now that we have the common ratio, we can find the 13th term by using the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
Where:
a_n = the nth term
a_1 = the first term
r = the common ratio
n = the term number
Given that a_1 = 7, r = -5, and n = 13:
a_13 = 7 * (-5)^(13-1)
a_13 = 7 * (-5)^12
a_13 = 7 * 244140625
a_13 = 1,708,984,375
Therefore, the 13th term of the sequence is 1,708,984,375.