#Confused102

Algebra Level pending

G i v e n t h e f i r s t f i v e t e r m s o f a s e q u e n c e , 1 , 6 , 84 , 1820 , 53130... W h a t i s t h e 6 t h t e r m ? Given\quad the\quad first\quad five\quad terms\quad of\quad a\quad sequence,\\ 1\quad ,\quad 6,\quad 84,\quad 1820,\quad 53130...\\ What\quad is\quad the\quad 6th\quad term?


The answer is 1947792.

Lance Joseph Esquejo by Lance Joseph Esquejo , 25, Philippines

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.

1 solution

I j u s t m a d e t h i s f o r m u l a . : ) a n = ( n 2 ) ! n ! ( n 2 − n ) ! S o t h e 6 t h t e r m i s : a 6 = ( 6 2 ) ! 6 ! ( 6 2 − 6 ) ! a 6 = ( 36 ) ! 6 ! ( 30 ) ! a 6 = 36 ∗ 35 ∗ 34 ∗ 33 ⋅ ⋅ ⋅ ⋅ ⋅ 2 ∗ 1 6 ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 × 30 ∗ 29 ∗ 28 ∗ 27 ⋅ ⋅ ⋅ ⋅ ⋅ 2 ∗ 1 a 6 = 36 ⋅ 35 ⋅ 34 ⋅ 33 ⋅ 32 ⋅ 31 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 a 6 = 1947792 I\quad just\quad made\quad this\quad formula.\quad :)\\ { a }_{ n }=\frac { ({ n }^{ 2 })! }{ n!({ n }^{ 2 }-n)! } \\ So\quad the\quad 6th\quad term\quad is:\\ \\ { a }_{ 6 }=\frac { ({ 6 }^{ 2 })! }{ 6!({ 6 }^{ 2 }-6)! } \\ { a }_{ 6 }=\frac { (36)! }{ 6!(30)! } \\ { a }_{ 6 }=\frac { 36*35*34*33\cdot \cdot \cdot \cdot \cdot 2*1 }{ 6*5*4*3*2*1\times 30*29*28*27\cdot \cdot \cdot \cdot \cdot 2*1 } \\ { a }_{ 6 }=\frac { 36\cdot 35\cdot 34\cdot 33\cdot 32\cdot 31 }{ 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1 } \\ { a }_{ 6 }=1947792

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...