Question

in an AP if the 12th term is - 13 and the sum of first 4 term is 24 what is the sum of the first 10 terms use formula

Answer 1

T12 = - 13

=> a + 11d = - 13

=> 2a + 22d = - 26 --------(1)

S4 = 24

=> T1 + T2 + T3 + T4 = 24

=> a + a + d + a + 2d + a + 3d = 24

=> 4a + 6d = 24

=> 2a + 3d = 12 -------(2)


On subtracting equation 2 from 1, we get


19d = - 38

=> d = - 2

Now,

On Substituting the value of d in equation 2, we get

=> 2a + 3(-2) = 12

=> 2a - 6 = 12

=> 2a = 18

=> a = 9


S10 = n/2 [ 2a + (n-1) d]

S10 = 10 /2 [ 2 × 9 + (10 - 1) (-2)]

S10 = 5 [ 18 + 9 (-2)]

S10 = 5 [ 18 - 18)

S10 = 5 × 0

S10 = 0

Sum of first 10 terms = 0

Answer 2

This question was answered by mysticd

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➡ https://brainly.in/question/1091847

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Let a and b are first term and

common difference of an A P.

n th term = tn = a+ ( n - 1 ) d

i) given t12 = - 13

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

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source: - https://brainly.in/question/1091847

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This answer was given by the mysticd





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