The sum of 4th and 8th term are of an Ap is 24 and the sum of 6th and 10th number is 44 find the Ap
Answers
Hey there!
Given,
4th term + 9th term = 24
a + (4-1)d + a +(9-1)d = 24
a + 3d + a + 8d = 24
2a + 11d = 24 ...............(i)
And,
6th term + 10th term = 44
a + (6-1)d + a +(10-1)d = 44
a + 5d + a + 9d = 44
2a + 14d = 44 .............(ii)
On subtracting equation (i) from (ii):
2a + 14d = 44
-2a - 11d = -24
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3d = 20
d = 20 / 3
Putting value of d in equation (i) :
2a + 11d = 24
2a + 11 * (20 / 3) = 24
2a + 220 / 3 = 24
2a = 24 * 3 / 220
a = (24 * 3) / (220 * 2)
a = 36 / 220
a = 18 / 110
a = 9 / 55
Now,
We know,
A.P series is given as:
a , a + d , a + 2d, ............
9/55 , (9/55 + 20 / 3), (9/55) + 2(20/3) ...........
9/55 , (27 + 1100)/ 165 , (27 + 2200) / 165 ...........
9 / 55 , 1127/ 165 , 2227/ 165.................
Hope It Helps You!
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.