two aps have the same commin difference the first term if one of these is 1 and of the other is 8then the difference between their is8then tje difference between their 4terms is?
Answers
Answer:
The difference between their 2nd terms = 5
ii. The difference between their 4th terms = 5
iii. The difference between their 10th terms = 5
iv. The difference between their 30th terms = 5
Explanation:
nth term of an Arithmetic progression is given by : a_n= a+(n-1)da
n
=a+(n−1)d
, where a= First term and d= common difference.
Given : Two AP have the same common difference.
The first term of one of these is 3 and that of the other is 8.
Then, the nth term of two APs will be :
a_n=3+(n-1)da
n
=3+(n−1)d
b_n=8+(n-1)db
n
=8+(n−1)d
First term for both APs.
a_2=3+da
2
=3+d
b_2=8+db
2
=8+d
Difference between their 2nd terms=b_2-a_2=8+d- 3-d=8-3=5b
2
−a
2
=8+d−3−d=8−3=5
Similarly , 4th terms
a_4=3+3da
4
=3+3d
b_4=8+3db
4
=8+3d
Difference between their 4th terms=b_4-a_4=8+3d- 3-3d=8-3=5b
4
−a
4
=8+3d−3−3d=8−3=5
Similarly , 10th terms
a_{10}=3+9da
10
=3+9d
b_{10}=8+9db
10
=8+9d
Difference between their 4th terms=b_{10}-a_{10}=8+9d- 3-9d=8-3=5b
10
−a
10
=8+9d−3−9d=8−3=5
Similarly , 30thth terms
a_{30}=3+29da
30
=3+29d
b_{30}=8+29db
30
=8+29d
Difference between their 4th terms=b_{30}-a_{30}=8+29d- 3-29d=8-3=5b
30
−a
30
=8+29d−3−29d=8−3=5
Therefore the answer of all options is 5