If the 12th tem of an A P is ndash 13 and the sum of the first four terms is 24 what is the sum of t...........

Quantitative Aptitude ( CCS) Arithmetic progression

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If the 12th tem of an A.P. is – 13 and the sum of the first four terms is 24, what is the sum of the first 10 terms?

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Explanation:

a + 11d = -13 ---------(1)
ii) sum of first 4 terms = 24
Sn = n/2 [ 2a + ( n-1 ) d ]
S4 = 24
4/2 [ 2a + 3d] = 24
2[2a + 3d ] = 24
2a + 3d = 12 ------------(2 )
Multiply equation ( 1 ) with 2 and subtract from (2)
We get -19 d = 38
d = -2
Put d value in (1)
a - 22 = -13
a = -13 + 22
a = 9
iii) a = 9 , d = -2 ,
n =10
S 10 = 10/2 [ 2 × 9 + ( 10 - 1 ) ( - 2 ) ]
= 5 [ 18 - 18 ]
= 5 × 0
= 0
Therefore,
Sum of first 10 terms = S 10 = 0