205k views
3 votes
Guess the rule and add the next number in the sequence.
1, 5, 13, 25, 41, ?

User Grabofus
by
8.0k points

1 Answer

4 votes

Suspect: we start adding 4, later 8, 12, 16...

Therefore, the next number is 41 + 20 = 61.

Now, we try to guess the rule.

Note that, the numbers that we add are multiples of 4. Try to write the sequence in a different way like this:

1, 1 +4, (1+4) +8, ((1+4)+8)+12, (((1+4)+8)+12) +16, ...

1, 1+4, 1 + 4(1+2), 1 + 4(1+2+3), 1+ 4(1+2+3+4)...

You must to know that 1+2+3+...+ n = n(n+1)/2

Then, the nth numbers of the sequence must to be 1 + 4n(n+1)/2 = 1+2n(n+1) = a_n

Check the formula:

n = 0 then a_0 = 1+ 0

n=1 then a_1 = 1 +2(2) = 5

n=2 then a_2 = 1 +2(2)(3) = 13

n=3 then a_3 = 1 +2(3)(4) = 25

n=4 then a_4 = 1 +2(4)(5) = 41

n=5 then a_5 = 1 +2(5)(6) = 61

....

User Mrksbnch
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories