Find the 12th term of the geometric sequence 2, -10 , 50
To find the 12th term of the geometric sequence, we first need to find the common ratio of the sequence.
The common ratio, r, can be found by dividing any term by the previous term. In this case, we can divide -10 by 2 to get:
r = -10/2 = -5.
Now that we know the common ratio is -5, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1).
In this case, a_1 = 2 and n = 12. Plugging in these values:
a_12 = 2 * (-5)^(12-1) = 2 * (-5)^11 = 2 * (-48828125) = -97656250.
Therefore, the 12th term of the geometric sequence is -97656250.