Question

Find 17th term of the sequence 5,5,11,29,65.....is?

Answer 1

Let's find the pattern to differences

5-5=0
11-5=6
29-11=18
65-29=36
and so on

sequence is 0,6,18,36,...
so pattern is 1*3*0,2*3*1,3*3*2,4*3*3...(n+1)*3*n,...

(n+1)3n=3n^2 + 3n

a0 = 5
a1 = a0 + 3*1^2 + 3*1=5 + 3+3 = 11
a2 = a1 + 3*2^2 + 3*2 = 11+3*4+6=29
a3 = a2 + 3*3^2 + 3*3 = 29 + 27+9=65

...


an = a(n-1) + 3*n^2 + 3n

...

17th term is

a16 = a15 + 3*16^2 + 3*16 = a15 + 816

The terms a4 through a15 can be determined easily using a spreadsheet program like excel or by hand.