The sum of 4th and 8th term of an AP is 24 and the sum of 6th and 10th term is 44 find the 3rd term of an AP
Answers
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 3 = a 2 + d = − 8 + 5 = −3
Answer:
- 13 , - 8 , - 3 .
Step-by-step explanation:
Let the first term a and common difference be d.
We know :
t_n = a + ( n - 1 ) d
t_4 = a + 3 d
t_8 = a + 7 d
We have given :
t_4 + t_8 = 24
2 a + 10 d = 24
a + 5 d = 12
a = 12 - 5 d ....( i )
t_6 = a + 5 d
t_10 = a + 9 d
: t_6 + t_10 = 44
2 a + 14 d = 44
a + 7 d = 22
a = 22 - 7 d ... ( ii )
From ( i ) and ( ii )
12 - 5 d = 22 - 7 d
7 d - 5 d = 22 - 12
2 d = 10
d = 5
We have :
a = 12 - 5 d
a = 12 - 25
a = - 13
Now required answer as :
- 13 , - 8 , - 3 .
Finally we get answer.