Which of these recursive formulas results in this sequence?

1, 3, 6, 10, 15, ...

A) an = 2a(n-1) – 1
B) an = 2a(n-1) + 1
C) an = a(n-1) – n
D) an = a(n-1) + n

Question

Which of these recursive formulas results in this sequence?

1, 3, 6, 10, 15, ...

A)   an = 2a(n-1) – 1
B)   an = 2a(n-1) + 1
C)   an = a(n-1) – n
D)   an = a(n-1) + n

anonymous · Answer

HI :DDD

anonymous · Answer

hi:)

tkhunny · Answer

3-1 = 2
6-3 = 3
10-6 = 4
15-10 = 5

I'm seeing a pattern.

anonymous · Answer

I do too but I don't understand which formula would match it.

tkhunny · Answer

A) an = 2a(n-1) – 1 -- Doubles and subtracts one.  Nope.
B) an = 2a(n-1) + 1 -- Doubles and subtracts one.  Nope.
C) an = a(n-1) – n -- Subtracts one more each step.  Nope.
D) an = a(n-1) + n -- Adds one more each time.  Maybe!

Have you considered trying to regenerate the sequence?

nipunmalhotra93 · Answer

the given sequence is a sequence of triangular numbers.. an=n(n+1)/2. It's better to use this than individually verifying the options.

tkhunny · Answer

Strongly Disagree.  Recognizing triangular numbers works ONLY for triangular numbers.  It is not a vry useful methodology.  Learning what it is doing and how to build it.  Learning how to use a recursive function.  Understanding what you are doing.  These are the more valuable methods.