Question

In an AP if
tm =n and tn=m then find tm+n

Answer 1

Answer:

0

Step-by-step explanation:

Given----> In an AP

mth term is n and nth term is m

To find---> (m+n )th term of AP.

Solution----> Let first term of AP be a and common difference be d.

Formula of pth term of AP is ,

aₚ = a + ( p - 1 ) d

ATQ, mth term of AP is n , so,

aₘ = n

Applying above formula for mth term , we get

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

ATQ, nth term of AP is m

=> aₙ = m

Apply above formula for nth term , we get,

=> a + ( n - 1 ) d = m .......................( 2 )

Now we solve these two equations

Subtracting equation ( 2 ) from equation ( 1 )

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

-a and a cancel out each other and we get,

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

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

-1 and 1 cancel out each other and we get,

=> ( m - n ) d = - ( m - n )

( m - n ) cancel out from both sides and we get,

=> d = - 1

Putting d = -1 in equation ( 1 ) we get,

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

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

=> a - ( m - 1 ) = n

=> a = m - 1 + n

=> a = m + n - 1

Now we calculate ( m + n )th term of AP,

( m+n )th term = a + ( m + n - 1 ) d

Putting a = ( m + n - 1 ) and d = -1 , we get,

= m + n - 1 + ( m + n - 1 ) ( - 1 )

= ( m + n - 1 ) - ( m + n - 1 )

= 0

#Answerwithquality

#BAL

Answer 2

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${ \huge \bf{ \mid{ \overline{ \underline{Answer}}} \mid}}$

$\huge\underline{\underline{\texttt{\purple{0 (Zero)}}}}$

#answerwithquality #bal