The sum of the 4th and 8th terms of an ap is 24 and sum of 6th and 10th term is 44 find ap
Answers
Answer:
Step-by-step explanation:
t4=a+3d. .........(1)
t8=a+7d. ..........(2)
t4+t8=a+5d.
12=a+5d. ......(3)
t6=a+5d. .......(4)
t10=a+9d. .......(5)
t6+t10=a+7d
22=a+7d. .........(6)
now(3)-(6)
d=5. & a=-13
AP is. -13,-8,-3,2......…..…
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.