Question

find nth term of the GP 3,-6,12,-24.........​

Answer 1

Answer:

nth term of a G.P. is given by the following expression:

a_{n} = a{r}^{n - 1}a

n

=ar

n−1

Here,

a = 3a=3

and,

r = \frac{a_n}{a_n -1}r=

a

n

−1

a

n

So,

r = \frac{6}{3} = 2r=

3

6

=2

3072 = 3. {2}^{n - 1}3072=3.2

n−1

{2}^{n - 1} = \frac{3072}{3} = 10242

n−1

=

3

3072

=1024

{2}^{n - 1} = {2}^{10}2

n−1

=2

10

n - 1 = 10n−1=10

Therefore,

n = 11n=11

Answer 2

In mathematics, a geometric progression (GP) is a type of sequence where each successive term is formed by multiplying each preceding term by a fixed number called a common ratio. This procedure is also known as a geometric sequence of numbers that follow a pattern. Learn arithmetic progression here too. The common ratio multiplied here by each term to get a next term is a non-zero number.

A geometric sequence or geometric sequence is a sequence in which each term is interchanged with another in a common ratio. The next term of the sequence is formed when we multiply a constant (which is non-zero) by the previous term. It is represented by:

$a, ar, ar^2, ar^3, ar^4....$ and so on.

Where a is the first term and r is the common ratio.

Note: It should be noted that when we divide any subsequent term by its previous term, we get a value equal to the common ratio.

Hence the nth term of G.P. is given by : $ar^{n-1}$

To find the nth term put n as n

In the given G.P. a=3 r=-2

Hence nth term can be given as

The nth term of G.P.= $3*(-2)^{n-1}$

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