Question

mean of sequence of 1 ,3,6,10,15...630

Answer 1

A triangular number or triangle numbercounts objects arranged in an equilateral triangle, as in the diagram on the right. Thenth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers (sequence A000217 in theOEIS), starting at the 0th triangular number, is

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...

Answer 2

Answer:

The mean of the sequence1, 3, 6, 10, 15...630 is 222.

Step-by-step explanation:

Given,

The sequence:

1, 3, 6, 10, 15...630

To find,

The Mean of the sequence.

Calculation,

We know that the sum of sequences with increasing common differences is

Sₙ = $\frac{\frac{n(n + 1)(2n + 1)}{6}+ \frac{n(n+1)}{2} }{2}$...(1)

But Last term = n(n + 1)/2

So, 630 = n(n + 1)/2

⇒ 1260 = n(n + 1)

⇒ n² + n - 1260 = 0

⇒ n = 35

Substituting n = 35 in equation (1):

$S_n = \frac{\frac{35(35 + 1)(2\times 35 + 1)}{6}+ \frac{35(35+1)}{2} }{2}$

⇒ Sₙ = 7770

Now the mean of the sequence is:
M = Sₙ/n

⇒ M = 7770/35

⇒ M = 222

Therefore, the mean of the sequence1, 3, 6, 10, 15...630 is 222.

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