Answer :

Formula Used.

d_{n} = a_{n + 1} – a_{n}

a_{n} = a + (n–1)d

In the above sequence,

a = 50;

d_{1} = a_{2}–a_{1} = 100–50 = 50

d_{2} = a_{3}–a_{2} = 150–100 = 50

d_{3} = a_{4}–a_{3} = 200–150 = 50

The difference in sequence is same and comes to be 50.

∴ The above sequence is A.P

The n^{th} term of A.P is a_{n} = a + (n–1)d

a_{n} = a + (n–1)d = 50 + (n–1)(50)

= 50 + 50n–50

= 50n

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