The sum 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.
Answers
Answer:
The A.P is -13 , -8, -3 , 2….
Step-by-step explanation:
Given :
a4 + a8 = 24 and a6 + a10 = 44
Let the first term of an A.P be 'a' and the common difference be 'd'.
By using the formula, an = a + (n - 1) d
Case : 1
a4 + a8 = 24
a + ( 4 - 1) d + a + ( 8 - 1) d = 24
a + 3d + a + 7d = 24
2a + 10d = 24
2(a + 5d) = 24
(a + 5d) = 24/2
a + 5d = 12 ………..(1)
Case : 2
a6 + a10 = 44
a + ( 6 - 1) d + a + ( 10 - 1) d = 44
a + 5d + a + 9d = 44
2a + 14d = 44
2(a + 7d) = 44
a + 7d = 44/2
a + 7d = 22…………….(2)
On Subtracting eq (i) & (ii),
a +7 d = 22
a + 5d = 12
(-) (-) (-)
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2d = 10
d = 5
On Putting the value of d = 5 in eq 1,
a + 5d = 12
a + 5 (5) = 12
a + 25 = 12
a = 12 - 25
a = - 13
First term , a = - 13
Second term , a2 = (a + d) = -13+5 = -8
Third term, a3 = (a + 2d) = -13 + 2× 5 = -13 + 10 = -3
Fourth term, a4 = (a + 3d) = - 13 + 3 × 5 = - 13 + 15 = 2
A.P -13 , -8, -3 , 2 …..
Hence, the A.P is -13 , -8, -3 , 2….
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