Question

3) Two AP's have same common
differences. The difference betser
sheir 100th term is 112233
What is the difference between their 1000th term
​

Answer 1

Let the common difference be 'd 'and the first terms of two A.Ps be a1 & a2

100th term it 1st A.P - 100th term of 2nd A.P = 111222333

(a1+99d)-(a2+99d) = 111222333

a1+99d-a2-99d = 111222333

(a1-a2) = 111222333

Difference between their millionth term

= (a1+99999d)-(a2+99999d)

= a1+99999d-a2-99999d

= a1-a2

= 111222333

Answer 2

$\large\bf\underline{Given:-}$

• Two AP's have same common
• differences. The difference betser
• sheir 100th term is 112233.

$\large\bf\underline {To \: find:-}$

• Difference between their 1000th term

$\huge\bf\underline{Solution:-}$

Two AP's have same common difference (d).

• Let the 1st term of 1st AP be a1
• Let the 2nd term of 2nd term be a2
• 100th term = a + 99d

Difference between their 100th term

= (a1 + 99d) - (a2 + 99d) = 112233

= a1 + 99d - a2 - 99d = 112233

= (a1 - a2 ) = 112233 .....(1)

Now,

• 1000th term = a + 999d

Difference between their 1000th term

= (a1 + 999d) - (a2 + 999d)

= a1 + 999d - a2 - 999d

= a1 - a2

From equation 1)

• a1 - a2 = 112233

Hence,

▶️ Difference between their 1000th term is 112233

$\rule{200}3$