What-is-the-next-term-in-the-below-sequence-1-3-9-27-81-243-729-2123-5857-

Question Number 3105 by prakash jain last updated on 04/Dec/15

What is the next term in the below sequence

1, 3, 9, 27, 81, 243, 729, 2123, 5857, ?

Commented by Filup last updated on 04/Dec/15

3^{10} ?

Commented by prakash jain last updated on 05/Dec/15

2123 \neq 3^{7}

Commented by Filup last updated on 05/Dec/15

\bar{} ∖ (^{∙} -^{∙}) / \bar{} \bar{}

You have me stumped on this one .

For now \dots

Commented by prakash jain last updated on 05/Dec/15

I was trying to highlight a point that given

a finite number of terms there are infinite

number of formula that can be defined to

generate the next term .

So if you were given only first 7 term the

obvious formula is 3^{n - 1}, while there may

be other formulas as well .

Commented by Rasheed Soomro last updated on 05/Dec/15

Y o u h a v e a n s w e r e d m y m i n d^{'} s q u e s t i o n b e f o r e e x p r e s s i n g!!

Commented by Rasheed Soomro last updated on 05/Dec/15

15203

Answered by Rasheed Soomro last updated on 06/Dec/15

1 3 9 27 81 243 729 2123 5857 \underline{\overset{(5857 - (- 9346)}{15203}}

- 2 - 6 - 18 - 54 - 162 - 486 - 1394 - 3734 \overset{(- 3734 - 5612)}{- 9346}

4 12 36 108 324 908 2340 \overset{(2340 - (- 3272)}{5612}

- 8 - 24 - 72 - 216 - 584 - 1432 \overset{(- 1432 - 1840)}{- 3272}

16 48 144 368 848 \overset{(848 - (- 992))}{1840}

- 32 - 96 - 224 - 480 \overset{(- 480 - 512)}{- 992}

64 128 256 \overset{(2^{9})}{512}

T h e l i n e s w r i t t e n i n b l a c k a r e t h e g i v e n s e q u e n c e

a n d d e r i v e d s e q u e n c e s . E a c h s e q u e n c i s m a d e b y

s u b t r a c t i o n o f c o n s e c u t i v e t e r m s o f p r e v i o u s

s e q u e n c e .

L a s t s e q u e n c e i s G P . I t s n e x t t e r m i s 512 .

P r e v i o u s t o t h e l a s t i s c a l c u l a t e d a s - 992

C a l c u l a t i n g n e x t t e r m s i n r e v e r s e o r d e r,

T h e n e x t t e r m o f t h e g i v e n s e q u e n c e i s 15203

Commented by Rasheed Soomro last updated on 05/Dec/15

T h e a b o v e a n s w e r c o u l d b e p o s s i b l e o n l y i n l i g h t o f y o u r

({p r a k a s h}^{'} s) g u i d a n c e!

Commented by prakash jain last updated on 06/Dec/15

Successive difference techinque is based on

the fact that it reduces degree of polynomials

and exponents by 1 .