Question

How To derive the formula for nth term of an AP

Answer 1

$a_{n} \: = a + (n - 1)d$

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Answer 2

Answer:

Formula for the nth term of an A.P. :

tn = a + ( n - 1 ) d

Step - by - step explanation:

Generally, in the A. P. t1, t2, t3,...... if the first term is 'a' and the common difference is 'd',

t1 = a

t2 = t1 + d = a + d = a + ( 2 - 1 ) d

t3 = t2 + d = a + d + d = a + 2d = a + ( 3 - 1 ) d

t4 = t3 + d = a + 2d + d = a + 3d = a + ( 4 - 1 ) d

∴ we get the formula

tn = a + ( n - 1 ) d