Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,
Find the 12th term of the geometric sequence 5, -25, 125,
no way that entire set of terms is a GP.
Taking just the 1st two terms, r = -5
So,
a12 = 5 * (-5)^11 = -5^12
Find the 12th term of following.-1,2,5
To find the 12th term of a geometric sequence, we need to know the first term (a) and the common ratio (r).
In this case, the first term (a) is 5. The common ratio (r) can be found by dividing any term by its previous term. If we divide -25 by 5, we get -5. Similarly, if we divide 125 by -25, we get -5. Therefore, the common ratio is -5.
To find the 12th term, we can use the formula for the nth term of a geometric sequence:
tn = a * r^(n-1)
Substituting the values into the formula, we get:
t12 = 5 * (-5)^(12-1)
= 5 * (-5)^11
Now, we can calculate this value by evaluating (-5)^11:
(-5)^11 = -48828125
Finally, we substitute this value back into the formula:
t12 = 5 * (-48828125)
= -244140625
Therefore, the 12th term of the geometric sequence 5, -25, 125, ... is -244140625.