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

The 11th term of an A.P. is 60 less than the 31st term of an A.P. . Find the common difference.

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.

If the 2^(nd) term of an A.P. is 8 and the 5 ^(th) term is 17, find its 19^(th) term.

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

Let 2^("nd"),8^("th") and 44^("th") terms of a non-constant A.P. be respectively the 1^("st"),2^("nd") and 3^("rd") terms of a G.P.If the first term of the A.P. is 1 ,then the sum of its first 20 terms is equal to -

Find four consecutive terms in an A.P. whose sum is 46 and the product of the 1st and the 3rd is 56. The terms are in ascending order.

The 11th term of an A.P. is 16 and the 21st term is 29 . Find the 16th term of this A.P.

If 2nd, 3rd and 6th terms of an AP are the three consecutive terms of a GP then find the common ratio of the GP.

If the 2^(nd) term of an A.P. is 13 and the 5^(th) term is 25, what is its 7 ^(th) term ?