Question

if the fourth term of a Gp is 3.Find the product of first 7 terms.

Answer 1

Let First term be a and common ratio be r.
Then According to question.

ar^3=3

Product of 1st 7 terms (a)^7(r)^21=(ar^3)^7
Hence answer is 3^7.

Answer 2

Answer:

The product of first 7 terms is 2187.

Step-by-step explanation:

Given : If the fourth term of a G.P is 3.

To find : The product of first 7 terms ?

Solution :

The seven terms of a G.P is $a,ar,ar^2,ar^3,ar^4,ar^5,ar^6$

The fourth term of G.P is $ar^3=3$

The product of first 7 terms is given by,

$S_7=a\times ar\times ar^2\times ar^3\times ar^4\times ar^5\times ar^6$

$S_7=a^7\times r^{21}$

$S_7=(ar^3)^7$

$S_7=(3)^7$

$S_7=2187$