the 8th term of an ap is 17 and its 14th term is 29. the common difference of the ap is
Solution:-
Given 8th term of an ap is 17.
Means, a8=17
a+7d=17 ..........(i)
and 14th term is 29
Means, a14=29
a+13d=29 ........(ii)
From equ (i) &(ii)
a+7d=17 ..........(i)
a+13d=29 ........(ii)
After solving,
d=2
Common difference=2 Ans
Q.The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Solution:-
Given 17th term of an AP exceeds its 10th term by 7
Means, a17=a10 +7
a +16d= a +9d+7
16d = 9d +7
16d -9d =7
7d=7
d=1
Common difference=1 Ans
Q.The sum of the 4th and the 8th term of an A.P. is 24 and the sum of the 6th and 10th terms of the A.P. is 34. Find the three terms of the A.P.
Solution:-
Given that the sum 4th and the 8th term of an A.P. is 24
Means, a4 + a8 = 24
a+3d+a+7d=24
2a + 10d = 24
a + 5d =12 ...............(i)
and the sum of the 6th and 10th terms of the sane A.P. is 34
Means, a6 + a10 = 34
a+5d+a+9d=34
2a + 14d = 34
a + 7d =17 ..............(ii)
From Equ (i) & (ii)
a + 5d =12 ...............(i)
a + 7d =17 ..............(ii)
After solving,
a= -1/2
d=5/2
the three terms of the A.P
first term=-1/2
second term
=a+d
=-1/2 + 5/2
=2
third term
= a+2d
=-1/2 +2 x 5/2
=-1/2 + 5
=9/2
the three term of AP's are -1/2,2,9/2
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
solution:-
Solution:-
Given that the 4th and the 8th term of an A.P. is 24
Means, a4 + a8 = 24
a+3d+a+7d=24
2a + 10d = 24
a + 5d =12 ...............(i)
and the sum of the 6th and 10th terms of the sane A.P. is 34
Means, a6 + a10 = 34
a+5d+a+9d=34
2a + 14d = 44
a + 7d =22 ..............(ii)
From Equ (i) & (ii)
a + 5d =12 ...............(i)
a + 7d =22 ..............(ii)
After solving,
a= -13
d=5
the three terms of the A.P
first term=-13
second term
=a+d
=-13 + 5
=-8
third term
= a+2d
=-13 +2 x 5
=-13 +10
=-3
the three term of AP's are -13,-8,-3 ans...
