find the nth term and the 10th term of a geometric sequence -7,14,-28,56...
the common ratio is -2
nth term = (-2)^(n-1) * -7
To find the nth term of a geometric sequence, we need to identify the common ratio (r) and the first term (a₁).
In the given sequence, we can observe that each term is obtained by multiplying the previous term by -2. We see that -7 × (-2) = 14, 14 × (-2) = -28, and so on. Therefore, the common ratio (r) is -2.
The first term (a₁) is given as -7.
The formula to find the nth term of a geometric sequence is:
an = a₁ * r^(n-1)
Using this formula, we can find the nth term. Let's find the 10th term (n = 10):
a10 = -7 * (-2)^(10-1)
= -7 * (-2)^9
= -7 * (-512)
= 3,584
Therefore, the 10th term of the geometric sequence -7,14,-28,56... is 3,584.
Now let's find the nth term. Substitute the desired value of n into the formula:
an = -7 * (-2)^(n-1)
So, in general, the nth term of the geometric sequence -7,14,-28,56... is -7 * (-2)^(n-1).