If 12th term of the ap is -13 and sum of its first four term is 24. what is sum of first ten terms?
If 12th term of the ap is -13 and sum of its first four term is 24. what is sum of first ten terms?
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We know that nth term of an AP an = a + (n - 1) * d.
(i)
Given : 12th term of the AP is -13.
⇒ a12 = a + (12 - 1) * d
⇒ -13 = a + 11d ----- (1)
(ii)
We know that Sum of first n terms of an AP is sn = n/2[2a + (n - 1) * d]
Given : sum of its first four term is 24.
⇒ s4 = (4/2)[2a + (4 - 1) * d]
⇒ 24 = 2[2a + 3d]
⇒ 12 = 2a + 3d ------ (2)
On solving (1) * 2 & (2) , we get
⇒ 2a + 22d = -26
⇒ 2a + 3d = 12
---------------------
19d = -38
d = -2
Substitute d = -2 in (2), we get
⇒ 12 = 2a + 3d
⇒ 12 = 2a + 3(-2)
⇒ 12 = 2a - 6
⇒ 18 = 2a
⇒ a = 9
Now,
Sum of first tern terms:
⇒ n/2[2a + (n - 1) * d]
⇒ 10/2[2(9) + (10 - 1) * (-2)]
⇒ 5[18 - 18]
⇒ 0.
Therefore, Sum of first ten terms = 0.
Hope this helps!