the sum of 4th and 8th term of Ap is 24 and the sum of 6th and 10th term is 44find the three term of AP
Answers
Step-by-step explanation:
Given:-
The sum of 4th and 8th term of Ap is 24 and the sum of 6th and 10th term is 44.
To find:-
Find the three terms of the AP?
Solution:-
We know that
a is the first term and d is the common difference of an AP then nth term = an = a+(n-1)d
4th term of the AP = a4 = a+(4-1)d
a4 = a+3d
6th term = a6 = a+5d
8th term = a8 = a+7d
10th term = a10 =a+9d
Now
Sum of 4th and 8 th terms = 24
=> a4+a8 = 24
=>a+3d+a+7d = 24
=>2a+10d = 24
=>2(a+5d) = 24
=>a+5d = 24/2
a+5d = 12------------(1)
and Sum of 6th and 10th terms = 44
=>a6+a10 = 44
=>a+5d+a+9d = 44
=>2a+14d =44
=>2(a+7d)=44
=>a+7d = 44/2
a+7d = 22---------(2)
On Subtracting (1) from (2) then
a+7d = 22
a+5d = 12
(-)
________
0+2d = 10
_________
=>2d = 10
=>d = 10/2
=>d = 5
On Substituting the value of d in (2) then
=>a+7(5)=22
=>a+35 = 22
=>a = 22-35
=>a = -13
We have a = -13 and d = 5
The first three terms of the AP are
a,a+d,a+2d
a= -13
a+d = -13+5 = -8
a+2d = -13+2(5)=-13+10=-3
Answer:-
The first three terms of the given AP are -13,-8,-3
Check:-
a4 = a+3d = -13+4(5)=-13+20=7
a8 = a+7d = -13+7(4)=-13+28=15
a4+a8 = 7+15 = 22
a6 = a+5d = -13+5(5)=-13+25=12
a10=a+9d = -13+9(5)=-13+45 = 32
a6+a10=12+32=44
Verified the given relations.
Used formulae:-
- a is the first term and d is the common difference of an AP then nth term = an = a+(n-1)d