Question

two arithmetic progression has the same common difference.If the first term of the first progression is 3 and that of the other is 8,then the difference between their 3rd term is​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Two A.Ps have the same common difference}$

$\textsf{First term of the first progression is 3}$

$\textsf{First term of the second progression is 8}$

$\underline{\textbf{To find:}}$

$\textsf{Difference between their 3rd terms}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the first A.P be A, A+d, A+2d, . . . }$

$\textsf{Let the second A.P be a, a+d, a+2d, . . . }$

$\textsf{Here, A=3 and a=8 }$

$\textsf{Difference between their 3rd terms}$

$\mathsf{=(A+2d)-(a+2d)}$

$\mathsf{=A+2d-a-2d}$

$\mathsf{=A-a}$

$\mathsf{=3-8}$

$\mathsf{=-5}$

$\underline{\textbf{Find more:}}$

The 7th and 17th term of an arithmetic progression are 33 and 83 respectively find the ap  

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Answer 2

Given : Two arithmetic progression has the same common difference.

 the first term of the first progression is 3 and that of the other is 8,

To Find : the difference between their 3rd term is​

Solution:

first term of the first progression is 3

Common difference = d

3 , 3 + d , 3 + 2d , _________

3rd term = 3 + 2d

first term of the 2nd progression is 8

Common difference = d   as same common difference.

8 , 8 + d , 8 + 2d , _________

3rd term = 8 + 2d

Difference = (3 + 2d) - ( 8 + 2d)  = -5

-5 is  the difference between their 3rd term is​

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