Question

two A.P'shave the same common difference.the first term of one A.P.is 4 and that of the other is 7.What is the difference between their i)7th term ii)20th term​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\huge\sf\pink{Answer}$

☞ For Both the Question your Answer is 3

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Two APs have the same common Difference

✭ The first term of one AP is 4 and the other is 7

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ Difference Between their 7th term

◈ Difference Between their 20thterm

$\rule{110}1$

$\huge\sf\purple{Steps}$

◕ First term of first AP = a₁ = 4

◕ First term of second AP = a₂ = 7

◕ Common Difference of both AP = d

So,

General term of first AP will be

➝ a₁ + ( n - 1 ) d

➝ $\sf\red{4 + ( n - 1 ) d}$

General term of second AP will be

➢ a₂ + ( n - 1 ) d

➢ $\sf\green{7 + ( n - 1 ) d }$

Now,

Difference Between their general terms will be,

»» 7 + ( n - 1 ) d - ( 4 + ( n - 1 ) d )

»» 7 + ( n - 1 ) d - 4 - ( n - 1 ) d

»» 7 - 4

»» $\sf\orange{3 }$

So,

Difference between the nth term of these two AP's will always be 3

$\rule{170}3$