Question

which of the following id the pyramidal number sequence?

A. 1, 2, 4, 8, 16, ...
B. 1, 4, 9, 16, 25, ...
C. 1, 5, 14, 30, 55, ...
D. 1, 1, 2, 3, 5, ...
E. 1, 3, 6, 10, 15, ..

Answer 1

* Which of the following is the pyramidal number sequence?

Answer 2

it isnt d

Answer 3

its b

Answer 4

Let S(n) be the nth square pyramidal number. S(n) is defined by the expression

S(n) = 1 + 4 + 9 + ... + (n-1)² + n². n terms

To find an explicit formula for this sum, consider the sum of n consecutive cubes from 2³ to (n+1)³, that is, the sum Σj=1...n(1+j)³.

Σj=1...n(1+j)³ = Σj=1...n(1 + 3j + 3j² + j³)

Σ(1+j)³ - Σj³ = Σ1 + 3Σj + 3Σj²

(1+j)³ - 1 = Σ1 + 3Σj + 3Σj²

(n+1)³ - 1 = n + 3n(n+1)/2 + 3Σj²

(n+1)³ - 1 - n - 3n(n+1)/2 = 3Σj²

n³ + 1.5n² + 0.5n = 3Σj²

n(n+1)(2n+1)/6 = Σj²

Thus, S(n) = n(n+1)(2n+1)/6.

Answer 5

does this help @sunnyday88

Answer 6

@sunnyday88
@sunnyday88
@sunnyday88

Answer 7

@KendrickLamar2014

Answer 8

@pooja195

Answer 9

@jigglypuff314

Answer 10

its b

Answer 11

its b



Let S(n) be the nth square pyramidal number. S(n) is defined by the expression

S(n) = 1 + 4 + 9 + ... + (n-1)² + n². n terms

To find an explicit formula for this sum, consider the sum of n consecutive cubes from 2³ to (n+1)³, that is, the sum Σj=1...n(1+j)³.

Answer 12

@mathmale

Answer 13

It was C but Thanks :)