Question

Find the 10th term of the geometric sequence 10, -20, 40, ...

Answer 1

Answer:

-5120

Step-by-step explanation:

deltamath

Answer 2

Given,

The geometric sequence: 10, -20, 40

To Find,

The 10th term =?

Solution,

We can solve the question as follows:

It is given that we have to find the 10th term of the geometric progression 10, -20, 40.

In a geometric progression, the ratio between two consecutive terms is always a constant. The common ratio is denoted by r.

Here,

$r = -\frac{20}{10} = -2$

Now, the nth term of a geometric progression is given as:

$T_{n} = ar^{n-1}$

Where,

$a = First\: term\\r = Common\: ratio\\n = nth\: term$

From the question,

$a = 10\\r = -2\\n = 10$

Substituing the values in the above formula,

$T_{n} = 10*(-2)^{10 - 1}$

     $= 10*(-2)^{9}$

     $= 10*(-512)$

     $= -5120$

Hence, the 10th term of the geometric progression is -5120.