Question
Sun December 25, 2011 By:

sir can you please show me the verification for the formula a+(n-1)d

Expert Reply
Sun December 25, 2011
The nth term of an AP is given by a + (n - 1)d, where a is the first term and d is the common difference of the AP.
Verification:
Let a1,a2, a3 ... be an AP whose first term is a1 and common difference is d.
 
Then,
Second term a2 = a + d = a + (2 – 1) d
Third term a3 = a2 + d = (a + d) + d = a + 2d = a + (3 – 1) d
Fourth term a4 = a3 + d = (a + 2d) + d = a + 3d = a + (4 – 1) d
and so on.
In general, nth term of an AP will be:
an = a + (n – 1) d
 
This verifies the formula of the nth term of the AP.
Ask the Expert