Solution
Let a and d is first term and common difference of the AP.
According to Question,
The 4 th and 8 th terms of an Ap are 11 and 23 .
Means, a4=11 & a8=23
now a4=11
a+3d=11 .......(i)
& a8=23
a+7d=23 .........(ii)
From Equation(i) & (ii)
a+3d=11 .......(i)
a+7d=23 .........(ii)
after solving,
a=2
and d = 3
Hence common difference=3 ans.....
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Solution
Let a and d is first term and common difference of the AP.
According to Question,
The 6th and 17th terms of an A.P. are 19 and 41
Means, a6=19 & a17=41
now a6=19
a+5d=19 .......(i)
& a17=41
a+16d =41.........(ii)
From Equation(i) & (ii)
a+5d=19 .......(i)
a+16d =41.........(ii)
after solving,
a=9
and d = 2
the 40th term=
means, a40=a+39d
a40=9+39×2
a40=87
Hence the 40th term=87 ans......
The 4 th term of an AP is 6 if the sum of the 8th and 9th terms is -72 the common difference is
Solution
Let a and d is first term and common difference of the AP.
According to Question,
The 4th term of an AP is 6.
Means, a4=6
a+3d = 6 .........(i)
and the sum of the 8th and 9th terms is -72.
Means, a8 + a9 =-72
a+7d + a+8d = -72
2a + 15d = -72 ........(ii)
From Equation(i) & (ii)
a+3d = 6 .........(i) ×2
2a + 15d = -72 ........(ii)
一一一一一一一
2a+6d =12 .........(i)
2a + 15d = -72 ........(ii)
一一一一一一一
After solving,
9d=84
d=84/9
d=28/3
Common Difference = 28/3 ans....
The first term of an AP is 5 and its 100th term is -292 find the 50th term of this AP
Solution
Let a and d is first term and common difference of the AP.
According to Question,
The first term of an AP is 5 .
means ,a=5
& 100th term is -292
Means, a100 = -292
a+99d=-292 ..........(i)
now, put value of a in Equation (i)
5+99d=-292
99d=-292-5
99d=-297
d= -297/99
d=-3
the 50th term of this AP
means, a50 = a+49d
a50 = 5+49×(-3)
a50 = 5- 147
a50 = -142
If five times the 5th term of an AP is equal to eight times its 8th term,then find its 13th term.
solution
Let a and d is first term and common difference of the AP.
According to Question,
five times the 5th term of an AP is equal to eight times its 8th term
means , 5a5 =8a8
now 5(a+4d) = 8(a+7d)
5a + 20d =8a +56d
5a-8a=56d-20d
-3a=36d
a=-12d
The 13th term of the AP=
a+12d
but a=-12d
so , -12d+12d =0
Hence 13th term of the AP = 0 ans....
The first and fourth terms of an AP are 3 and 1.5 respectively then the 8th term of the AP is
Solution
Let a and d is first term and common difference of the AP.
According to Question,
The first and fourth terms of an AP are 3 and 1.5
Means, a=3 & a4=1.5
now a4=1.5
a+3d=1.5 .......(i)
now, put value of a in Equation (i)
3+3d=1.5
3d=1.5-3
3d=-1.5
d=-0.5
the 8th term of the AP is
means, a8=a+7d
a8=3+7×(-0.5)
a8=3+7×(-0.5)
a8=-0.5
Hence the 8th term of the AP is -0.5 Ans......
The sum of the 8th and 9th term of an arithmetic progression is 72, and the 4th term is -6. What is the common difference?
Solution
Let a and d is first term and common difference of the AP.
According to Question,
The sum of the 8th and 9th term of an arithmetic progression is 72
Means, a8 + a9 =72
a+7d+a+8d =72
2a + 15d = 72 ...............(i)
and the 4th term is -6 .
a4 = -6
a+3d = -6 ..............(ii)
From Equ (i) & (ii)
2a + 15d = 72 ...............(i)
a+3d = -6 ..............(ii) ×2
一一一一一一一一一一一一
2a + 15d = 72 ...............(i)
2a+6d = -12 ..............(ii)
一一一一一一一一一一一一
After solving,
9d=84/3
d=28/3
The common difference=28/3
