In an A.P. the m times of m^th term is equal to n times the n^th term, its (m + n)^th term will be

Question

Question

This question was previously asked in

RPSC 2nd Grade Mathematics (Held on 18th Feb 2019) Official Paper

Answer 1

Given:

In an A.P. the m times of mth term is equal to n times the nth term

Concept used:

n^th term of A.P = a_n = a + (n - 1)d

Calculation:

According to question,

⇒ m × a_m = n × a_n

⇒ m[a + (m - 1)d] = n[a + (n - 1)d]

ma + m(m - 1)d = na + n(n - 1)d

ma + m²d - md = na + n²d - nd

a(m - n) + (m² - n²)d = d(m - n)

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

∴ [a + d(m + n - 1] = 0 = a_{m + n}

∴ a_{m + n}= 0

∴ (m + n)th term will be 0.

Download Solution PDF