Fibonacci sequences

Number Theory Level 1

510 , 965 , 1475 , 2440 , 3915 , 6355 , 10270 , 16625 , 26895 , ______ 510,\ 965,\ 1475,\ 2440,\ 3915,\ 6355,\ 10270,\ 16625,\ 26895,\ \text{\_\_\_\_\_\_}

What comes next?

43520 43550 44444 54459

Munem Shahriar by Munem Shahriar , 18, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Chew-Seong Cheong
Mar 20, 2017

The sequence is a Fibonacci-like sequence , where the general formula of the terms is a n = a n − 1 + a n − 2 a_n = a_{n-1} + a_{n-2} as shown below.

510 + 965 = 1475 965 + 1475 = 2440 1475 + 2440 = 3915 2440 + 3915 = 6355 3915 + 6355 = 10270 6355 + 10270 = 16625 10270 + 16625 = 26895 16625 + 26895 = 43520 \begin{aligned} 510+965 & =1475 \\ 965+1475&=2440 \\ 1475+2440&=3915 \\ 2440+3915&=6355 \\ 3915+6355&=10270 \\ 6355+10270&=16625 \\ 10270+16625&=26895 \\ 16625+26895&=\boxed{43520} \end{aligned}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Why need of the formula a n = a n − 1 + a n − 2 ? a_n = a_{n-1} + a_{n-2}? .Just add first number and the second number ..... and so on.

Munem Shahriar - 4 years ago

Log in to reply

Just add the first number and second number and so on means a 1 + a 2 = a 3 a_1 + a_2= a_3 , a 2 + a 3 = a 4 a_2+a_3=a_4 , ⟹ a n − 2 + a n − 1 = a n \implies a_{n-2}+a_{n-1}=a_n .

Chew-Seong Cheong - 4 years ago
Munem Shahriar
Mar 19, 2017

510+965=1475

965+1475=2440

1475+2440=3915

2440+3915=6355

3915+6355=10270

6355+10270=16625

10270+16625=26895

16625+26895=43520

Ans..43520

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Jul 21, 2017

The sequence is a Fibonacci-like sequence,cz,

at first, 510+965=1475

then , 965+1475=2440

next,2440+ 1475=3915

this pattern is going in this way, so, the wanted value will be=16625+26895=43520

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...