0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Show that the sum of (m+n)th and (mn)th terms of an A.P. is equal to twice the mth term.

Solution
Verified by Toppr

Let a and d be the first term and the common difference of A.P. respectively.
It is known that the kth term of an A.P. is given by
ak=a+(k1)dam+n=a+(m+n1)damn=a+(mn1)dam=a+(m1)dam+n+amn=a+(m+n1)d+a+(mn1)d=2a+(m+n1+mn1)d=2a+(2m2)d=2a+2(m1)d=2[a+(m1)d]=2am
Hence proved.

Was this answer helpful?
0
Similar Questions
Q1
Show that the sum of (m+n)th and (mn)th terms of an A.P. is equal to twice the mth term.
View Solution
Q2
Show that the sum of (m+n)th and (mn)th term of an A.P. ie equal to twice the mth terms.
View Solution
Q3
Sum of (m+n)th and (mn)th term of an A.P. is equal to twice the mth term.
View Solution
Q4
If m times the mth term of an A.P. is equal to n times nth term, show that the (m+n)th term of the A.P. is zero.
View Solution
Q5
If m times mth term of an A.P. is equal to n times its nth term, then show that (m+n)th term of the A.P. is zero
View Solution