Question

if m time the mth term of an A.P is equal to n time the nth term and it,s (m+n)th term X then the value of 24967x is:-

a. 1/2
b. 1
c. -1
d. 0​

Answer 1

✪ANSWER✪

• d) 24967X = 0

★EXPLAINATION★

☆GIVEN☆

• $m\times a_{m} = n\times a_{n}$
• $a_{m+n} = X$

☆TO FIND☆

• 24967X

☆CALCULATION☆

Let a and d be the first term and common difference of the AP,

$m\times a_{m} = n\times a_{n}$

$⇒m[a+(m-1)d] = n[a+(n-1)d]$

$⇒ma+m(m-1)d] = na+n(n-1)d]$

$⇒(ma - na) + (m² - n²)d - (m - n)d = 0$

$⇒a(m- n) + (m- n)(m+n)d - (m - n)d = 0$

$⇒(m- n)[a + (m+n)d - d] = 0$

Since m≠n ⇒ m-n ≠ 0

$⇒[a + (m+n)d - d] = 0$

$⇒[a + (m+n - 1)d] = 0$

$⇒a_{m+n} = 0$

$⇒24967a_{m+n} = 0$