nth term (I)

Algebra Level 2

12th term of the sequence $0, 2, 8, 24, 64, . . .$ is?

22528 106496 49152 10240

1 solution

Zeeshan Ali
Jan 25, 2015

general term of the sequence 0, 2, 8, 24, 64, . . . . is (n-1) (2^(n-1)) for n=12; 12th term is (11) 2^(11)=22528

It is f(1)=0 and f(2)=2 ... and for n>=3 ...

The relation is f(n) = 4{ f(n-1) -f(n-2) ]

To confirm just use the formula...

f(3) = 4( 2-0) = 8

f(4) = 4(8 -2) = 24

f(5) = 4( 24 -8) = 64

f(6) = 4( 64 - 24) = 160

f(7) = 4( 160 -64) = 384

f(8) = 4( 384 - 160) = 896

f(9) = 4( 896 -384) = 2048

f(10) = 4( 2048 - 896) = 4608

f(11) = 4( 4608 -2048) = 10240

So , f(12) = 4(10240 - 4608) = 22528.

Its option no. (1) [22528]

Nihar Mahajan - 6 years, 4 months ago

SURELY RIGHT ANSWER

Zeeshan Ali - 6 years, 4 months ago

So , both 49152 and 22528 are correct?

Nihar Mahajan - 6 years, 4 months ago

Note that since your first term is 0, your general term is actually $(n-1) 2^{ n-1 }$ .

I have updated the answewr to 22528. Please update your solution accordingly.

Calvin Lin Staff - 6 years, 4 months ago

@Calvin Lin is my solution correct?

Nihar Mahajan - 6 years, 4 months ago