If the fourth and the sixth terms of a geometric progression are 8 and 1/2 respectively, then the first term of this sequence will be;

The first term of the sequence is 512 or -512

Step-by-step explanation:

Geometric Progression

The general term n of a geometric progression of first term a1 and common ratio r is:

We are given:

Applying the equation for n=4:

We have:

Applying the equation for n=6:

We have:

Dividing [2] by [1]:

Operating:

Taking the square root:

There are two possible solutions:

From [1]:

This gives also two possibles solutions for a1:

Thus, the first term of the sequence is 512 or -512

a

step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: