here is question for you all solve this if you can.
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Here is your solution
Let,
The first term of an A.P.=a
The common difference of the given A.P.=d
As we know that,
a n = a + (n − 1) d
a 4 = a + (4 − 1) d
a 4 = a + 3d
Similarly,
a 8 = a + 7d
a 6 = a + 5d
a 10 = a + 9d
Sum of 4th and 8th term = 24 (Given)
a 4 + a 8 = 24
a + 3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12.................... (i)
Sum of 6th and 10th term = 44 (Given)
a 6 + a 10 = 44
a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22 ......................(ii)
from equation 1st and 2 on solving we get
d=5
From equation (i), we get,
a + 5d = 12
a + 5 (5) = 12
a + 25 = 12
a = −13
a 2 = a + d = − 13 + 5 = −8
a 3 = a 2 + d = − 8 + 5 = −3
∴The first three terms of this A.P. are −13, −8, and −3.
We know that nth term of an AP an = a + (n - 1) * d
Given that sum of 4th term and 8th term of an AP is 24.
(i) 4th term = a + (4 - 1) * d = a + 3d.
(ii) 8th term = a + (8 - 1) * d = a + 7d.
Now,
⇒ a + 3d + a + 7d = 24
⇒ 2a + 10d = 24
⇒ a + 5d = 12 -------- (1)
Given that 6th term and 10th term of an AP is 44.
(i) 6th term a6 = a + (6 - 1) * d = a + 5d.
(ii) 10th term a10 = a + (10 - 1) * d = a + 9d
Now,
⇒ a + 5d + a + 9d = 44
⇒ 2a + 14d = 44
⇒ a + 7d = 22 -------- (2)
On solving (1) & (2), we get
⇒ a + 5d = 12
⇒ a + 7d = 22
-----------------
2d = 10
d = 5.
Substitute d = 5 in (1), we get
⇒ a + 5d = 12
⇒ a + 5(5) = 12
⇒ a + 25 = 12
⇒ a = -13.
Hence,
First term = -13.
Second term = -13 + 5 = -8.
Third term = -8 + 5 = -3.
Therefore, the AP is -13,-8,-3.
Hope this helps!