The sum of the 4th term and the 8th term of an A. P. is 24 and the sum of the 6th and the 10th is 44. Find the first three terms of the A. P.
The sum of the 4th term and the 8th term of an A. P. is 24 and the sum of the 6th and the 10th is 44. Find the first three terms of the A. P.
the first term of an A.P.=a
and 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)
Solving (i) and (ii), we get,
a + 7d = 22
a + 5d =12
on substracting
2d = 10
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
the first term of an A.P.=a
and 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)
Solving (i) and (ii), we get,
a + 7d = 22
a + 5d =12
on substracting
2d = 10
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
