Question

What is the next term of the geometric sequence? 3, 12, 48,

Answer 1

Answer:

192

Step-by-step explanation:

Answer 2

The next term of the geometric sequence 3 , 12 , 48 is 192

Given :

The geometric sequence 3 , 12 , 48

To find :

The next term of the geometric sequence

Concept :

For a geometric sequence

The nth term of the geometric sequence is given by

$\displaystyle \sf{ }t_n = a \times {r}^{n - 1}$

Where , first term = a and common ratio = r

Solution :

Step 1 of 2 :

Find first term and common ratio

Here the given geometric sequence is 3 , 12 , 48

First term = a = 3

Common ratio = r = 12/3 = 4

Step 2 of 2 :

Find next term of the geometric sequence

Next term of the geometric sequence

= 4th term of the geometric sequence

$\displaystyle \sf{ = t_4 }$

$\displaystyle \sf{ = a \times {r}^{ 4- 1} }$

$\displaystyle \sf{ = a \times {r}^{3} }$

$\displaystyle \sf{ = 3 \times {4}^{3} }$

$\displaystyle \sf{ = 3 \times 64 }$

$\displaystyle \sf{ = 192 }$

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