All poem of term 2nd

The first term of a G.P. is -3. If the 4th term of this G.P. is the square of the 2nd term, then find its 7th term.

Find the 4 terms in G .P. in which 3rd term is 9 more than the first term and 2nd term is 18 more than the 4th term.

The sum of the 2nd term and the 7th term of an A.P. is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P.

Prove that the product of the 2nd and 3rd terms of an A.P. exceeds the product of the 1st and 4th by twice the square of the difference between the 1st and 2nd.

The 2nd, 31st and last term of an A.P. are 7(3)/(4) , (1)/(2) and -6(1)/(2) respectively. Find the first term and the number of terms.

If in the expansion of (1/x+xtanx)^5 the ratio of 4^(th) term to the 2^(nd) term is 2/27pi^4 , then value of x can be

The number of terms of a G.P. are even. If the sum of all terms of the series is 5 times the sum of all terms at odd positions, then find the common ratio.