The next term of the G.P. `x ,x^2+2,a n dx^3+10` is `(729)/(16)` b. `6` c. `0` d. `54`

Find the 10th and pth terms of the G.P. {2, 6, 18, 54,…}

Find the 6th and nth term of the GP 2, 6, 18, 54,.....

Find the next two terms of the series 2,-6,18,-54,.....

If the 4th term in the expansion of (a x+1//x)^n is 5/2, then a. a=1/2 b. n=8 c. a=2/3 d. n=6

In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coefficients of x^5a n dx^(10) is zero , then n is a. 25 b. 20 c. 15 d. none of these

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 x ,2x+2 and 3x+3 are the first three terms of a G.P., then the fourth term is a. 27 b. -27 c. 13.5 d. -13.5

If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G.P, then the common ratio of the G.P. is a. 3 b. 1/3 c. 2 d. 1/2

In a sequence of (4n+1) terms, the first (2n+1) terms are n A.P. whose common difference is 2, and the last (2n+1) terms are in G.P. whose common ratio is 0.5 if the middle terms of the A.P. and LG.P. are equal ,then the middle terms of the sequence is (n .2 n+1)/(2^(2n)-1) b. (n .2 n+1)/(2^n-1) c. n .2^n d. none of these

If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0 are in the ratio a. 1/2(-1+isqrt(3)) b. 1/2(1-isqrt(3)) c 1/2(-1-isqrt(3)) d. 1/2(1+isqrt(3))