Q. 14.0( 12 Votes )

# If the n^{th} term of a sequence is given by a_{n} = n^{2} – n+1, write down its first five terms.

Answer :

Given,

a_{n} = n^{2} – n+1

We can find first five terms of this sequence by putting values of n from 1 to 5.

When n = 1:

a_{1} = (1)^{2} – 1 + 1

⇒ a_{1} = 1 – 1 + 1

⇒ a_{1} = 1

When n = 2:

a_{2} = (2)^{2} – 2 + 1

⇒ a_{2} = 4 – 2 + 1

⇒ a_{2} = 3

When n = 3:

a_{3} = (3)^{2} – 3 + 1

⇒ a_{3} = 9 – 3 + 1

⇒ a_{3} = 7

When n = 4:

a_{4} = (4)^{2} – 4 + 1

⇒ a_{4} = 16 – 4 + 1

⇒ a_{4} = 13

When n = 5:

a_{5} = (5)^{2} – 5 + 1

⇒ a_{5} = 25 – 5 + 1

⇒ a_{5} = 21

∴ First five terms of the sequence are 1, 3, 7, 13, 21.

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