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Progressions

by harsh.champ » Mon Feb 08, 2010 5:10 am
Sum of the first 30 terms of an arithmetic progression is 0. If the first term is -29, then find the sum of the 28th, 29th and 30th terms of this arithmetic progression.

(A)81
(B)84
(C)-84
(D)-81
(E)None of these

The OA is A.
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by shashank.ism » Mon Feb 08, 2010 5:32 am
harsh.champ wrote:Sum of the first 30 terms of an arithmetic progression is 0. If the first term is -29, then find the sum of the 28th, 29th and 30th terms of this arithmetic progression.

(A)81
(B)84
(C)-84
(D)-81
(E)None of these

The OA is A.

Let the common difference of the arithmetic progression be 'd'.
a=-29
S=n/2 (2a +(n-1)d)=0

Sum of first 30 terms of the arithmetic progression
=30/2 [2x(-29) + (30-1) d]

⇒15(−58+29d)=0
⇒d=2
Sum of 28th, 29th and 30th term of this arithmetic progression
= 3(-29) + (27 + 28 +29) × 2 = 81
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