(iii) In a finite AP ; the sum of the terms equidistant from the beginning and end is always same and is equal to the sum of first and last terms.

Show that in an A.P.the sum of the terms equidistant from the beginning and end is always same and equal to the sum of first and last terms.

(iv) In a finite GP the product of the terms equidistant from the beginning and end is always same and is equal to the product of first and last term.

Statement -1: If a_(1),a_(2),a_(3), . . . . .,a_(n), . . . is an A.P. such that a_(1)+a_(4)+a_(7)+ . . . .+a_(16)=147 , then a_(1)+a_(6)+a_(11)=98 Statement -2: In an A.P., the sum of the terms equidistant from the beginning and the end is always same and is equal to the sum of first and last term.

In a finite G.P.the product of the terms equidistant from the beginning and the end is always same and equal to the product of first and last term.

In the A.P.1,7,13,19, ; 415 prove that the sum of the middle terms is equal to the sum of first and last terms.

In an A.P, the sum of first 2n terms is equal to the sum of next n terms. Then the ratio of the sum of first 3n terms to the next n terms is

If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p+q) terms.

If the sum of the first 9 terms of an AP is equal to the sum of its first 11 terms, then find the sum of its first 20 terms.