Question

If m times the mth term of an AP is equal to the n times nth term then show that the (m + n ) th term of the AP is zero

Answer 1

Answer:

Let a be the first term and let d be the common difference.  Then...

m times the mth term of is equal to the n times nth term

=> m ( a + (m-1)d ) = n ( a + (n-1 )d )

=> (m-n)a + [ m(m-1) - n(n-1) ] d = 0

=> (m-n)a + [ m² - n² - m + n ] d = 0

=> (m-n)a + [ (m-n)(m+n) - (m-n) ] d = 0

=> a + (m+n-1)d = 0           ... (*)

=> the (m + n)-th term is zero.

Note: In line (*), we have assumed that m≠n.  This additional assumption is necessary as the claim is not true if m=n.

Answer 2

Answer:

He or she is right.

Step-by-step explanation: