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How do you find the first five terms given #a_1=6# and #a_(n+1)=a_n+n+3#?

Answer 1

James Allen

First five term are #{6,10,15,21,28,......}#

As #a_(n+1)=a_n+n+3#

#a_2=a_1+1+3=6+1+3=10#

#a_3=a_2+2+3=10+2+3=15#

#a_4=a_3+3+3=15+3+3=21#

#a_5=a_4+4+3=21+4+3=28#

Hence first five term are #{6,10,15,21,28,...........}#

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Answer 2

Lincoln Anderson

To find the first five terms of the sequence defined by ( a_1 = 6 ) and ( a_{n+1} = a_n + n + 3 ), we can use the recursive formula provided.

We'll start with ( a_1 = 6 ), and then apply the recursive formula to find each subsequent term.

( a_1 = 6 )
( a_2 = a_1 + 1 + 3 = 6 + 1 + 3 = 10 )
( a_3 = a_2 + 2 + 3 = 10 + 2 + 3 = 15 )
( a_4 = a_3 + 3 + 3 = 15 + 3 + 3 = 21 )
( a_5 = a_4 + 4 + 3 = 21 + 4 + 3 = 28 )

So, the first five terms of the sequence are: 6, 10, 15, 21, 28.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.