the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.
Answers
Answered by
44
Let 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,

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.
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,

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.
Answered by
7
Solution :-
Given :-
The sum of 4th and 8th terms of an AP is 24.
the sum of 6th and 10th terms is 44
To find first 3 terms of the AP.
First term of an A.P = a
common difference of the given A.P= d
we know that,
tn = a + (n − 1) d
a 4 = a + (4 − 1) d
a 4 = a + 3d
again
a 8 = a + 7d
a 6 = a + 5d
a 10 = a + 9d
Sum of 4th and 8th term = 24 (Given)
A/q
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/q
a 6 + a 10 = 44
a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22 ......................(ii)
On 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✔
Hence,
The first three terms of this A.P. are −13, −8, and −3 .
Thanks.
Given :-
The sum of 4th and 8th terms of an AP is 24.
the sum of 6th and 10th terms is 44
To find first 3 terms of the AP.
First term of an A.P = a
common difference of the given A.P= d
we know that,
tn = a + (n − 1) d
a 4 = a + (4 − 1) d
a 4 = a + 3d
again
a 8 = a + 7d
a 6 = a + 5d
a 10 = a + 9d
Sum of 4th and 8th term = 24 (Given)
A/q
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/q
a 6 + a 10 = 44
a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22 ......................(ii)
On 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✔
Hence,
The first three terms of this A.P. are −13, −8, and −3 .
Thanks.
Similar questions