The geometric series a + ar + ar 2+ ar 3+ ldots ldots . ∞ has a sum of 7 and the terms involving odd powers of r has a sum of 3. The value of (a+r) equals

Question

The geometric series a + ar + ar 2+ ar 3+ ldots ldots . ∞ has a sum of 7 and the terms involving odd powers of r has a sum of 3. The value of (a+r) equals (A) 4 / 3 (B) 10 / 7 (C) 5 / 2 (D) 7 / 3

Tardigrade Admin · Accepted Answer

( a /1- r )=7....(1) and ( ar /1- r 2)=3 ......(2) solving r =3 / 4 and a =7 / 4 ⇒ a + r =5 / 2

Q. The geometric series $a + a r + a r^{2} + a r^{3} + \dots\dots .\infty$ has a sum of 7 and the terms involving odd powers of $r$ has a sum of 3. The value of $(a + r)$ equals

$4/3$

$10/7$

$5/2$

$7/3$

$\frac{a}{1 - r} = 7$ ....(1)
and $\frac{a r}{1 - r ^{2}} = 3$ ......(2)
solving $r = 3/4$ and $a = 7/4$
$\Rightarrow a + r = 5/2$

Q. The geometric series a+ar+ar2+ar3+…….∞ has a sum of 7 and the terms involving odd powers of r has a sum of 3. The value of (a+r) equals

4/3

10/7

5/2

7/3