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3 The sum of 4th and 8th terms of an A.P is sum of 6th and 10th term of the same A.P is 44. Find the first 3 terms
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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,
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
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