Question

An Arithmetic Progression consists of 13 terms. The sum of the three middle most terms is 135 and the sum of the last three terms is 240. Find A.P.

Answer 1

Given,

An arithmetic progression consists of 13 terms. The sum of the three middle most terms is 135 and the sum of the last three terms is 240.

To find,

Arithmetic progression.

let a is first and d is common difference.

then, a , a + d , a + 2d , a + 3d , .... a + 12d are 13 terms in ap.

A/C to question,

The sun of three middle most term = 135

⇒6th + 7th + 8th = 135

⇒{a+ (6 - 1)d} + {a + (7 - 1)d} + {a + (8 - 1)d} = 135

⇒3a + (5 + 6 + 7)d = 135

⇒a + 6d = 45 ..........(1)

Again, The sum of the last three terms = 240

⇒11th + 12th + 13th = 240

⇒{a + (11 - 1)d} + {a + (12 - 1)d} + {a + (13 - 1)d} = 240

⇒3a + (10 + 11 + 12)d = 240

⇒a + 11d = 80.........(2)

from equations (1) and (2) we get,

5d = 35 ⇒d = 7

a = 80 - 11d = 80 - 77 = 3

therefore arithmetic progression is ; 3 , 10, 17, 24, ...... 87