Question

two AP have the same common difference. The first term of one of these is 3 and that of the other is 8. what is the difference between their
i. 2nd terms?
ii. 4th terms?
iii. 10th terms?
iv. 30th terms?
​

Answer 1

i. 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 : $a_n= a+(n-1)d$

, 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 :

$a_n=3+(n-1)d$

$b_n=8+(n-1)d$

First term for both APs.

$a_2=3+d$

$b_2=8+d$

Difference between their  2nd terms=$b_2-a_2=8+d- 3-d=8-3=5$

Similarly , 4th terms

$a_4=3+3d$

$b_4=8+3d$

Difference between their  4th terms=$b_4-a_4=8+3d- 3-3d=8-3=5$

Similarly ,  10th terms

$a_{10}=3+9d$

$b_{10}=8+9d$

Difference between their  4th terms=$b_{10}-a_{10}=8+9d- 3-9d=8-3=5$

Similarly , 30thth terms

$a_{30}=3+29d$

$b_{30}=8+29d$

Difference between their  4th terms=$b_{30}-a_{30}=8+29d- 3-29d=8-3=5$

Therefore the answer of all options is 5.

#Learn more :

If the nth term of AP 9,7,5....is same as the nth term of 15,12,9....Find n​

https://brainly.in/question/10449785

Answer 2

Step-by-step explanation:

hope it will help you