The sum of the first and the fifth term of an ascending AP is 26 and the products of the - Maths - Arithmetic Progressions

Question

The sum of the first and the fifth term of an ascending AP is 26
and the products of the second term by the fourth term is 160 Find
the sum of the first seven terms of this AP

Brijendra Pal · Accepted Answer

Hi, The sum of first and fifth term of AP = 26 a+a+4d = 26 2a+4d = 26a+2d = 13
1product of 2nd and 4th term = 160 a+da+3d= 160 13-d13+d= 160 Using equatoin 1 169-d2= 160 d2= 9 d = 3 neglect -3 as here AP is ascendingso a = 13-2d = 7 Now sum of first 7 term Sn= n22a+n-1dS7=7214+6×3=16×7=112

The sum of the first and the fifth term of an ascending AP is 26 and the products of the second term by the fourth term is 160. Find the sum of the first seven terms of this AP.