Question

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

Answer 1

Answer:

The sum of first 10 terms is 0 .

Step-by-step explanation:

Given :  

a12 = -13 , S4 = 24

By using the formula ,an = a + (n - 1)d

a12 = a + (12 – 1) d

a + 11d = -13

a = -13 - 11d …………(1)

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

S4 =  [2a + (4 – 1) d]

24 = 2 [2a + 3d]

24/2 = [2a + 3d]

12 = 2a + 3d

12 = 2 (-11d – 13) + 3d

12 = - 22d – 26 + 3d

22d -  3d  = - 26 - 12

19d = - 38

d = -38/2

d = -2

On putting the value of d = -2 in equation 1,  

a = -13 - 11d

a = -13 - 11(-2)

a = - 13 + 22

a = 9

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

S10 = 10/2 [2(9) + (10 – 1) (-2)]

S10 = 5 [18 - 18]

S10 = 5 [18 – 18]

S10 = 0

Hence, the sum of first 10 terms is 0 .

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Answer 2

Answer: 0

Step-by-step explanation:

Given :  

a12 = (-13) & S4 = 24

Using the formula:

an = a + (n - 1)d

» a12 = a + (12 - 1) d

» a + 11d = -13

» a = -13 - 11d ___(1)

Now,

Using the formula,

Sn = n/2 (2a + (n - 1) d)

» S4 =  (2a + (4 - 1) d)

» 24 = 2 (2a + 3d)

» 12 = 2a + 3d

» 12 = 2 (-11d - 13) + 3d.. (From 1)

» 12 = - 22d - 26 + 3d

» 22d -  3d  = - 26 - 12

» 19d = - 38

» d = -2

Putting the value of d in (1),  

» a = -13 - 11d

» a = -13 - 11(-2)

» a = - 13 + 22

» a = 9

Now, To find sum of 10 terms,

Sn = n/2 [2a + (n – 1) d]

» S10 = 10/2 (2(9) + (10 – 1) (-2))

» S10 = 5 (18 - 18)

» S10 = 0

Thus, the sum of first 10 terms of A.P is 0.