Question

Sum of 6 terms of AP is 90. Sum of first two terms is diminished by 32 with the sum of last two terms find the terms of AP.

Answer 1

terms of AP are ; 5 , 9, 13 , 17, 21 , 25 ....

let first term of an AP is a and common difference is d.

given, sum of first 6 terms is 90.

⇒6/2 [2a + (6 - 1)d ] = 90

⇒3[2a + 5d ] = 90

⇒2a + 5d = 30.........(1).

similarly, sum of first two terms + 32 = sum of last two terms

⇒a + (a + d) + 32 = {a + (6 - 1)d } + {a + (6 - 1 - 1)d}

⇒2a + d + 32 = 2a + 9d

⇒d = 32/8 = 4

from equations (1) we get,

2a = 30 - 20 = 10

a = 5

hence, a = 5 and d = 4

now Arithmetic progression are ; 5, 9, 13, 17, 21, 25.....