Consider an infinite geometric series with first term `a` and common ratio `r`. If its sum is 4 and the second term is 3/4, then (a)`a=4/7, r=3/7` (b). `a=2, r=3/8` (c). `a=3/2, r=1/2` (d). `a=3, r=1/4`

In an infinite geometric series S=(2)/(3) and t_(1)=(2)/(7) . What is r?

The sum of an infinite geometric series with positive terms is 3 and the sums of the cubes of its terms is (27)/(19) . Then the common ratio of this series is

Write down the series whose r^(th) term is 3. 2 ^(r + 1 ) . Is it a geometric series ?

Find the sum of first 20 terms of an A.P., in which 3r d terms in 7 and 7t h term is tow more than thrice of its 3r d term.

Let a+a r_1+a r1 2++ooa n da+a r_2+a r2 2++oo be two infinite series of positive numbers with the same first term. The sum of the first series is r_1 and the sum of the second series r_2dot Then the value of (r_1+r_2) is ________.

Let a+a r_1+a r1 2++ooa n da+a r_2+a r2 2++oo be two infinite series of positive numbers with the same first term. The sum of the first series is r_1 and the sum of the second series r_2dot Then the value of (r_1+r_2) is ________.

Let T_r be the rth term of an A.P. whose first term is -1/2 and common difference is 1, then sum_(r=1)^n sqrt(1+ T_r T_(r+1) T_(r+2) T_(r+3))

With usual notations in a triangle A B C , if r_1=2r_2=2r_3 then 4a=3b (b) 3a=2b 4b=3a (d) 2a=3b

Consider a G.P. with first term (1+x)^(n) , |x| lt 1 , common ratio (1+x)/(2) and number of terms (n+1) . Let S be sum of all the terms of the G.P. , then sum_(r=0)^(n)"^(n+r)C_(r )((1)/(2))^(r ) equals (a) 3/4 (b) 1 (c) 2^n (d) 3^n

If the sum of infinite positive G.P. is 3 and sum of cubes of there terms is 27/19 then common ratio of G.P. is equal to (A) 1/3 (B) 2/3 (C) 5/7 (D) 1/4