Question

Please help so urgent....
( 1). 4th term of an AP is equal to 3 times its first term and 7th term exceeds twice the 3rd term by 1 .find first term and common difference.
(2). The sum of the 2nd term and the 7th term of an AP is 30. If its 15th term I 1 less than twice of its 8th term, find the AP
(3). In an AP if mth term is n and nth term is m,show that its rth term is ( m+ n- r)

Answer 1

There is an AP, The 4th term is three times the first. So the relation is

3a = a + 3d, or

2a = 3d, or

a = (3/2)d …(1)

The 7th term exceeds twice the third term by 1. The relation is

a+6d = 2(a+2d)+1, or

a + 6d = 2a+4d+1, or

2a-a = 6d-4d-1, or

a = 2d-1 …(2). Equate (1) and (2)

a = (3/2)d = 2d-1, or

3d = 4d-2, or

4d-3d=2, or d = 2 and a = 3.

The first term is 3 and the common difference is 3.

Check: The series of the AP is 3,5,7,9,11,13,15.

The 4th term is 9, which is three times the first term. Correct.

The 7th term is 15, which is twice the third term plus 1. Correct.