If the nth term of a sequence is given by an = n2 – n+1, write down its first five terms.
Given,
an = n2 – n+1
We can find first five terms of this sequence by putting values of n from 1 to 5.
When n = 1:
a1 = (1)2 – 1 + 1
⇒ a1 = 1 – 1 + 1
⇒ a1 = 1
When n = 2:
a2 = (2)2 – 2 + 1
⇒ a2 = 4 – 2 + 1
⇒ a2 = 3
When n = 3:
a3 = (3)2 – 3 + 1
⇒ a3 = 9 – 3 + 1
⇒ a3 = 7
When n = 4:
a4 = (4)2 – 4 + 1
⇒ a4 = 16 – 4 + 1
⇒ a4 = 13
When n = 5:
a5 = (5)2 – 5 + 1
⇒ a5 = 25 – 5 + 1
⇒ a5 = 21
∴ First five terms of the sequence are 1, 3, 7, 13, 21.