Question

two APS have a same common difference the difference between the 100 term is 100 what is the difference between their 1000 term
Please answer​

Answer 1

Answer:

100

Step-by-step explanation:

Let the difference be d,

And the first term of AP1 be a1

And AP 2 be a2

100th term of AP1 is a1+99d……(i)

100th term of AP2 is a2+99d……(ii)

ATQ,

(i) - (ii) =100

i.e,

a1-a2=100

Now,

1000th term of AP1 is a1+999d……(iii)

1000th term of AP2 is a2+999d……(iv)

(iii)-(iv)=100

i.e a1-a2=100

Therefore the difference between their 1000th term is 100

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Answer 2

Answer:

Let the first term of these A.P.s be a1 and a2 respectively and the common difference of these A.P.s be d.

For first A.P.,

a100 = a1 + (100 − 1) d

= a1 + 99d

a1000 = a1 + (1000 − 1) d

a1000 = a1 + 999d

For second A.P.,

a100 = a2 + (100 − 1) d

= a2 + 99d

a1000 = a2 + (1000 − 1) d

= a2 + 999d

Given that, difference between

100th term of these A.P.s = 100

Therefore, (a1 + 99d) − (a2 + 99d) = 100

a1 − a2 = 100 (1)

Difference between 1000th terms of these A.P.s

(a1 + 999d) − (a2 + 999d) = a1 − a2

From equation (1),

This difference, a1 − a2 = 100

Hence, the difference between 1000th terms of these A.P. will be 100