The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms of the AP.
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Answers
Answer:
-18,-3,-8
Step-by-step explanation:
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)
Solving (i) and (ii), we get,
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
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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)
Solving (i) and (ii), we get,
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
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