Question

Write the nth
term of an AP1/m,1+m/m,1+2/m,......

Answer 1

Your question needs a correction.

Correct equation : 1 / m , ( 1 + m ) / m , ( 1 + 2m ) / m .....

Answer:

Step-by-step explanation:

Given equation : 1 / m , ( 1 + m ) / m , ( 1 + 2m ) / m.....

From the given sequence :

First term = a = 1 / m

Second term = a + d = ( 1 + m ) / m

Common Difference = a + d - a

                   ⇒ ( 1 + m ) / m - 1 / m

                   ⇒ ( 1 + m - 1 ) / m

                   ⇒ m / m

                   ⇒ 1

From the identities of arithmetic progressions,

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

$\therefore \text{nth\:term } = \dfrac{1}{m}+ ( n - 1 )1$

$\implies \text{nth\:term } = \dfrac{1+(n-1)m}{m}$

Therefore, the value of nth term of the AP is { 1 + ( n - 1 )m } / m .