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Find out the next number in following Simple series,

15, 55, 120, 210, 325, ?, ?

Note: Question has many solutions.

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closed as too broad by dmg, leoll2, Rand al'Thor, JLee, Aggie Kidd May 11 '15 at 14:47

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ It's 5 times 3,11,24,42,65,... $\endgroup$ – Rand al'Thor May 9 '15 at 10:43
  • $\begingroup$ explain more! what's this series 3,11,24,42,65.... $\endgroup$ – Saurabh Prajapati May 9 '15 at 10:46
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    $\begingroup$ A lot of answers, and not the simple one: it's the sequence containing every 5th triangle number. $\endgroup$ – Phylogenesis May 9 '15 at 13:00
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    $\begingroup$ You shouldn't add a solution to your question. There's a button at the bottom to "answer your own question" if this is what you want to do. $\endgroup$ – Rand al'Thor May 9 '15 at 13:01
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    $\begingroup$ OEIS A144312 $\endgroup$ – Tryth May 9 '15 at 13:07
5
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Answer is:

465

Because:

You add 5 to the factor of 5 being added. Between first two you add $5 \times 8$, next one you add $5 \times 13$, then $5 \times 18$, then $5 \times 23$, so next you add $5 \times 28$, ending with $5 \times 93 = 465$.

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3
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It's

$$465$$

Because:

$$t_n=\frac{5}2n(n+5)$$

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  • $\begingroup$ Are you sure??? $\endgroup$ – Saurabh Prajapati May 9 '15 at 12:08
  • $\begingroup$ @SaurabhPrajapati yes. $\endgroup$ – RE60K May 9 '15 at 15:52
  • $\begingroup$ @SaurabhPrajapati In which way my answer is different or wrong than the accepted answer. $\endgroup$ – RE60K May 13 '15 at 4:52
1
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You start by (adding) 15, so you have 15. From then you keep adding the same number as before plus 25.

Therefore the sequence is:

$$15,55,120,210,325,465,630$$

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  • $\begingroup$ sorry , but i can't understand? please explain more.. $\endgroup$ – Saurabh Prajapati May 9 '15 at 12:37
  • $\begingroup$ You first add 15 (from 0), then 15+25=40, then 40+25=65, then 65+25=90, and so on. $\endgroup$ – Masclins May 9 '15 at 12:38
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    $\begingroup$ your answer and logic both are Right! $\endgroup$ – Saurabh Prajapati May 9 '15 at 12:57

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