Question

The common difference of two Arithmetic Progressions is equal. If the first term of the first Arithmetic Progression is 6 and the first term of the second Arithmetic Progression is 10 then the difference of the 5th term of these Arithmetic Progressions is​

Answer 1

Step-by-step explanation:

above is the explanation of given question

Answer 2

Answer:

The difference in 5th term of both the arithmetic progressions is 4.

Step-by-step explanation:

Given that,

The common difference of two Arithmetic Progressions is equal.

Also given that,the first term of first arithmetic progression is 6 and the first term of the second arithmetic progression is 10.We are required to find the difference of 5th term of these arithmetic progressions.

Let the common difference of both the arithmetic progressions be d

Let the first terms of both the progressions be $a_{1}=6\\b_{1}=10$

For an arithmetic progression,the nth term in the series is $a_{n}=a+(n-1)d$

Hence,for first progression-The 5th term is $a_{5}=a_{1}+(5-1)d=6+4d$

Similarly,for the second progression we have $b_{5}=b_{1}+(5-1)d=10+4d$

Hence the difference between the two terms is

$= > b_{5}-a_{5}=(10+4d)-(6+4d)=4$

Therefore,the difference in 5th term of both the arithmetic progressions is 4.

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