in an ap if the 12th term is -13 and the sum of its first four terms is 24.find the sum of its first 10 terms
Answers
Answer:
Step-by-step explanation:
a12 = a +11d =-13
sum of 4 = (4/2)(a+a+3d)
4a + 6d = 24
2a + 3d = 12
2a + 22d = -26
19d = -38
d=-2
2a -6 = 12
a= 9
sum of 10 terms = (10/2)(a + a +9d)
= 5 * (2a + 9d)
= 5 * (18 - 18)
= 0
☞ In an AP, if the 12th term is - 13.
= a + (n - 1)d
Here
= - 13
n = 12
= a + (12 - 1)d
=> - 13 = a + 11d
=> a + 11d = - 13
=> a = - 13 - 11d ________(eq 1)
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☞ Sum of first four term is 24.
= [2a + (n - 1)d]
Here
= 24
n = 4
= [2a + (4 - 1)d]
=> 24 = 2 (2a + 3d)
=> 12 = 2a + 3d
=> 2a + 3d = 12
=> 2(- 13 - 11d) + 3d = 12
=> - 26 - 22d + 3d = 12
=> - 19d = 12 + 26
=> - 19d = 38
=> d = -2
Put value of d in (eq 1)
a = - 13 - 11 (-2)
=> - 13 + 22
=> 9
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☞ We have to find the sum of first 10 term.
= [2a + (10 - 1)d]
=> 5 (2a + 9d)
Now put the value of a and d in above eq
=> 5 [2(9) + 9(-2)]
=> 5 ( 10 - 10)
=> 5 (0)
=> 0
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The sum of first 10 term is 0.
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