the fourth term of a ap is 11 . the sum of the fifith and seventh term of an ap is 24 , find its common difference
Answers
a+3d=11
a=11-3d...... EQ 1
a5+a7=24
(a+4d)+(a+6d)=24
2a+10d=24
put EQ 1
2(11-3d)+10d=24
22-6d+10d=24
4d=2
d=1/2
common difference=1/2
Given,
The fourth term of the A.P. = 11
Sum of the fifth term and seventh term = 24
To find,
The common difference of the A.P.
Solution,
The common difference of the A.P. will be 1/2.
We can easily solve this problem by following the given steps.
According to the question,
The fourth term of the A.P. (a4) = 11
Sum of the fifth term and seventh term (a5 + a7) = 24
a4 = 11
We know that the formula to find the nth term is a+(n-1)d.
a4 = a+(4-1)d
a4 = a+3d --- equation 1
a5 + a7 = 24
a +(5-1)d + a+(7-1)d = 24
a+4d+a+6d = 24
2a+10d = 24
Taking 2 commons from the 2a and 10d,
2(a+5d) = 24
a+5d = 24/2 ( 2 was in the multiplication on the left-hand side. So, it is in the division on the right-hand side.)
a+5d = 12 --- equation 2
Subtracting equation 2 from equation 1,
(a+5d)-(a+3d) = 12-11
a+5d-a-3d = 1
2d = 1
d = 1/2
Hence, the common difference of the A.P. is 1/2.