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 product of 3rd and 8th terms of a G.P. is 243 and its 4th term is 3. Find its 7th term.

If the 3rd and the 6th terms of an A.P. are 7 and 13 respectively, find the first' term and the common difference.

Determine 2nd term and 5'th term of an A.P. whose 6th term is 12 and 8th term is 22

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.

The product of 5 terms of G.P. whose 3rd term is 2 is

Given that the (p+1)th term of an A.P. is twice the (q+1)th term, prove that the (3p+1)th term is twice the (p+q+1)th term.

Find the 31st term of an A.P. whose 10th term is 38 and 16th term is 74.

In the expansion of (1 + x)^n if the 2nd and 3rd terms are respectively a,b then x =

If the sum of first 3 terms of an A.P. is 33 and their product is 1155 . Then the 11^(th) term of the A.P . Is

Two A.P have the same common difference. The first term of one A.P is 2 and that of the other is 7. The difference between the 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any corresponding terms. Why?