Question

sum of the infinite terms of a G. P. is 12. If the first term is 8, find the fourth term of this G.P. ​

Answer 1

Answer:

8/27

Explanation:

Given:

• S = 12
• a = 8

To find:

• T4?

Solution:

S = a/(1-r)

12 = 8/(1-r)

12(1-r) = 8

12-12r = 8

12-8 = 12r

4 = 12r

r = 4/12

r = 1/3

Tn = ar^(n-1)

T4 = ar^3

T4 = 8×(1/3)^3

T4 = 8×1/27

T4 = 8/27

Answer 2

Answer:

      The fourth term is $\frac{8}{27}$ .

Explanation:

        The sum of infinite terms is

                             $s_{n} =\frac{a}{1-r}$

                             $12=\frac{8}{1-r}$

                                $3=\frac{2}{1-r}\\3(1-r)=2\\3-3r=2\\3-2=3r\\1=3r\\r=\frac{1}{3}$

                                $t_{n} =ar^{n-1} \\t_{4} =ar^{4-1}\\=ar^{3} \\=8(\frac{1}{3})^{3} \\ =\frac{8}{27}$