Question

Write the explicit formula for the geometric sequence given the following: a4 = 12, r = 2

Answer 1

Answer:

The explicit formula is  : $a_n = (1.5)(2)^{(n-1)}$

Step-by-step explanation:

Here, in the given GP sequence,

a(4)  = 12, r  = 2

Now, the general term in a  geometric sequence is given as:

$a_n = ar^{(n-1)}$

Now, here substituting the value of n = 4 , we get:

$a_4 = ar^{(\\4-1)}\\\implies a_4 = ar^3 = a(2)^3 = a \times 8 \\\implies a _4 = 8 a\\\implies 12 = 8 a\\\implies a = 12/8 = 1.5$

So, here the first term (a) in the sequence = 1.5

So, the explicit formula is given as :

$a_n = (1.5)(2)^{(n-1)}$

Hence, the explicit formula is  : $a_n = (1.5)(2)^{(n-1)}$