Question

Two AP s have same common difference . Difference between their 50th term is 60, W
What is the difference between their 500th term.

Answer 1

$\rule{400}4$

☆ ANSWER:-

▪︎ Given:-

• Two Aps have same common difference.

• Difference between their 50th term is 60.

▪︎ To Find:-

• The difference between their 500th term.

$\rule{400}2$

▪︎ Formula Used:-

$\tt\leadsto a_n = a+(n-1)d.$

Where,

• $\sf a_n = {n}^{th} term$
• a = First Term.
• d = Common Difference.
• n = number of terms.

$\rule{400}2$

▪︎ So,

• Let the common difference of both the APs be d.

• Let the first term of first AP be a.

• Let the first term of second AP be b.

▪︎ Now, ATQ:-

$\tt\mapsto a_{50} - b_{50} = 60 \\ \\ \tt\mapsto \: (a + (50 - 1)d) - (b + (50 - 1)d) = 60 \\ \\ \tt\mapsto(a + 49d) - (b + 49d) = 60 \\ \\ \tt\mapsto \: a \cancel{+ 49d} - b \cancel{ - 49d} = 60 \\ \\ \tt(by \: ope ning \: brackets) \\ \\ \tt\leadsto \: a - b = 60...eq(1)$

$\rule{400}2$

▪︎ Thus,

• Difference between their 500th term,

$\sf =a_{500}-b_{500} \\ \\ \sf = (a + (500 - 1)d) - (b + (500 - 1)d \\ \\ \sf = (a + 499b) - (b + 499d) \\ \\ \sf = a\cancel{ + 499d} - b \cancel{ -499d} \\ \\ \sf(by \: ope ning \: brackets) \\ \\ \sf = a - b \\ \\ \sf = 60 \\ \\ \sf(from \: eq(1))$

$\rule{400}4$

▪︎ Therefore The difference between their 500th term = 60.

$\rule{400}4$