Find-the-nth-term-for-the-sequence-3-12-27-48-75-

Question Number 109858 by aurpeyz last updated on 26/Aug/20

Find the nth term for the sequence 3 . 12 . 27 . 48 . 75 \dots

Answered by Her_Majesty last updated on 26/Aug/20

3 n^{2}

Answered by 1549442205PVT last updated on 26/Aug/20

Since the Difference of degree 2 is

constant, the general terms has the

form u_{n} = {an}^{2} + bn + c . Give n the

values 1, 2, 3 \dots

Commented by aurpeyz last updated on 26/Aug/20

Pls what do you mean give n the value 1 2 3 ?

how will that give us the answer

Commented by 1549442205PVT last updated on 28/Aug/20

n = 1 \Rightarrow a . 1^{2} + b . 1 + c = 3, n = 2 \Rightarrow a . 2^{2} + b . 2 + c = 12

n = 3 \Rightarrow a . 3^{2} + b . 3 + c = 27 . We obtain a

system of three eqs . of degree 1 for 3

unknowns a, b, c . Solve this system

Answered by bemath last updated on 26/Aug/20

3; 12; 27; 48; 75; \dots

9; 15; 21; 27

6; 6; 6;

U_{n} = 3 + (n - 1) . 9 + \frac{(n - 1) (n - 2)}{2!} . 6

U_{n} = 9 n - 6 + 3 (n^{2} - 3 n + 2)

U_{n} = 3 n^{2} + 9 n - 9 n - 6 + 6 = 3 n^{2}

Commented by Ari last updated on 26/Aug/20

Dear can you explain to me more clearly how you came to the general formula Un

Commented by aurpeyz last updated on 26/Aug/20

I will also like to know please .

Commented by aurpeyz last updated on 26/Aug/20

I will also like to know if i can use this approach

for any kind of question ?

Commented by aurpeyz last updated on 27/Aug/20

i t b i s t h e f o r m u l a i s N e w t o n F o r w a r d D i f f r e n c e F o r m u l a

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