Question

the first term of GP is 2 , and the sum to infinity is 6 .find the common ratio??​

Answer 1

Answer:

Sum of infinite G.P=

$\frac{a}{1 - r}$

Step-by-step explanation:

Given,

$\frac{a}{1 -r } = 6$

So,

$\frac{2}{6} =1 - r$

$r = 1 - \frac{1}{3}$

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

Answer 2

Value of common ratio(r) is 2/3.

Given:

• First term of GP is 2 , and
• The sum to infinity is 6.

To find:

• Find the common ratio.

Solution:

Formula to be used:

Sum of GP upto infinty: $\bf S_{\infty} = \frac{a}{1 - r}$

here, a: first term and r:common ratio.

Step 1:

Write the given values.

$a = 2$

$S_{\infty} = 6$

Step 2:

Put the values in the formula and find r.

$6 = \frac{2}{1 - r}$

or

$6(1 - r) = 2$

or

$3(1 - r) = 1$

or

$3 - 3r = 1$

or

$- 3r = 1 - 3$

or

$3r = 2$

or

$\bf \red{r = \frac{2}{3}}$

Thus,

Value of common ratio(r) is 2/3.

Learn more:

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