Question

Write the sixth to tenth term of the sequence whose nth term is
a_n=(n(n-1))/((n+3))

Answer 1

Answer:The series is: (3,3,6,9,15,24,..)

Taking 3 common from each term it becomes:

(1,1,2,3,5,8) [i.e a fibonacci sequence]

To know more click Fibonacci series.

The tenth term of this new series will be 55.

So, The tenth term of the given series will be,

=3*55

=165

Explanation:

The sequence is,

3,3,(3+3),{(3+3)+3},{(3+3),(3+3+3)},….

=(3*1),(3*1),(3*(1+1)),(3*(1+2)),(3*(2+3)),

(3*(3+5)),(3*(5+8)),(3*(8+13)),…

=(3*1),(3*1),(3*2),(3*3),(3*5),(3*8),(3*13),(3*21),…

So, the 10 th term will be,

3*(21+(21+13))

=3*55

=165

Step-by-step explanation: