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The twelfth term of an AP is -13 and the sum of its first four terms is 24. Find the sum of its first 10 terms.

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-5

-10

answer is B.

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Detailed Solution

It is given that the 12th term is -13 and the sum of its first four terms is 24.
From the given information,

a 12 = − 13

.
The nth term of an AP is given by,

a n = a + (n − 1) d

.
Substitute the known values in the formula.

a + 11 d = − 13

a = − 13 − 11 d

……(1)
And

S 4 = 24

.
The formula which gives the sum of the formula is,

S n = n 2 [2 a + (n − 1) d]

.
Substitute the known values in the formula.

24 = 42 [2 a + (4 − 1) d]

24 = 2[2a + 3d]

2 a + 3 d = 12

……(2)
Substitute (1) in (2),

2 (− 13 − 11 d) + 3 d = 12

− 26 − 22 d + 3 d = 12

− 19 d = 38

d = -2
Find the value of a by substituting the value of d in equation (1),

a = − 13 − 11 (− 2)

a = 22 − 13

a = 9

The formula that gives the sum of the n terms is,

S n = n 2 [2 a + (n − 1) d]

.
By substituting the known values,

S 10 = 102 [2 (9) + (10 − 1) (− 2)]

= 5 [18 − 18]

= 0

The sum of the terms is 0.
Hence, option 2) is correct.

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