Find-the-nth-term-of-this-sequence-3-18-45-84-135-

Question Number 12226 by tawa last updated on 16/Apr/17

Find the nth term of this sequence

3, 18, 45, 84, 135 \dots

Answered by ajfour last updated on 16/Apr/17

T_{n} = 3 n (2 n - 1) .

Commented by tawa last updated on 16/Apr/17

Workings plesse! \dots God bless you .

Commented by mrW1 last updated on 16/Apr/17

3 = 3 \times 1 \times 1

18 = 3 \times 6 = 3 \times 2 \times 3

45 = 3 \times 15 = 3 \times 3 \times 5

84 = 3 \times 28 = 3 \times 4 \times 7

135 = 3 \times 45 = 3 \times 5 \times 9

\Rightarrow 3 \times n \times (2 n - 1)

Commented by ajfour last updated on 16/Apr/17

1 \times 3, 2 \times 9, 3 \times 15, 4 \times 21, 5 \times 27, . .

3 [1 \times 1, 2 \times 3, 3 \times 5, 4 \times 7, 5 \times 9, . .]

s o 3 n (2 n - 1) .

Commented by tawa last updated on 16/Apr/17

God bless you sir .

Answered by sandy_suhendra last updated on 16/Apr/17

the n th term Un = {an}^{2} + bn + c

if n = 1 \Rightarrow a + b + c = 3 \dots . (1)

if n = 2 \Rightarrow 4 a + 2 b + c = 18 \dots (2)

if n = 3 \Rightarrow 9 a + 3 b + c = 45 \dots . (3)

(2) - (1) \Rightarrow 3 a + b = 15 \dots . (4)

(3) - (2) \Rightarrow 5 a + b = 27 \dots . (5)

(5) - (4) \Rightarrow 2 a = 12 \Rightarrow a = 6

substitute to (4) \Rightarrow 3 (6) + b = 15 \Rightarrow b = - 3

substitute to (1) \Rightarrow 6 - 3 + c = 3 \Rightarrow c = 0

so Un = {6 n}^{2} - 3 n

Commented by sandy_suhendra last updated on 16/Apr/17

we can use Un = {an}^{2} + bn + c

for the sequence like this

1, 2, 5, 10, 17, \dots

2, 4, 8, 14, 22, \dots

3, 18, 45, 84, \dots

Commented by tawa last updated on 16/Apr/17

God bless you sir

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