The sum of 4th and 8th terms of an AP is 24 and sum of the 6th and 10th terms is 44 .find the first three trems of the AP
Answers
Answer:
-13 , - 8 , - 3
Step-by-step explanation:
Given ---> Sum of 4th and 8th terms of AP be 24 and sum of 6th and 10th terms are 44
To find ---> First three terms of AP
Solution --->We know that formula for nth term of AP is
aₙ = a + (n -1 ) d
Given
Sum of fourth term and eighth term is 24
=> a₄ + a₈ = 24
=> a + ( 4 - 1 ) d + a + ( 8 - 1 ) d = 24
=> a + 3 d + a + 7d = 24
=> 2a + 10 d = 24
dividing whole equation by 2 we get
=> a + 5 d = 12
=> a = 12 - 5d ............(1)
ATQ , Sum of sixth term and tenth term is 44
a₆ + a₁₀ = 44
=> a + ( 6 - 1 ) d + a + ( 10 - 1 ) d = 44
=> a + 5 d + a + 9 d = 44
=> 2a + 14 d = 44
Dividing whole equation by 2 we get
=> a + 7 d = 22
Putting a = 12 - 5d in it we get
=> 12 - 5 d + 7 d = 22
=> 2 d = 22 - 12
=> 2 d = 10
=> d = 10 / 2
=> d = 5
Putting d = 5 in equation (1) we get
a = 12 - 5 d
=> a = 12 - 5 (5)
=> a = 12 - 25
=> a = -13
First term = a = -13
Second term = a₂
= a₁ + d
= -13 + 5
= - 8
Third term = a₂ + 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.