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

Question

Two A.P's have 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

Explanation

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

= 4 + ( n - 1 ) d

general term of second AP will be

= a₂ + ( n - 1 ) d

= 7 + ( n - 1 ) d

Now,

difference between their general terms (with same value of n) will be

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

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

= 7 - 4

= 3

so,

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

Therefore,

difference b/w their 7th terms = 3

difference b/w their 20th term = 3 .