An=(An-1)3-4; A1=2 What are the first three terms of a sequence?
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Answer:
(i) We have, a
n
=3n+2
Putting n=1,2 and 3, we get
a
1
=3×1+2=3+2=5
a
2
=3×2+2=6+2=8
a
3
=3×3+2=9+2=11
Thus, the required first three terms of the sequence defined by a
n
=3n+2 are 5,8 and 11.
(ii) We have a
n
=n
2
+1
Putting n=1,2 and 3, we get
a
1
=1
2
+1=1+1=2,
a
2
=2
2
+1=4+1=5,
and, a
3
=3
2
+1=9+1=10.
Thus, the first three terms of the sequence defined by a
n
=n
2
+1 are 2,5 and 10.
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