Question 1168283
<br>
Follow the instructions to find the first 5 terms recursively:<br>
a(1) = 3
a(2) = 2*a(1)+5 = 6+5 = 11
a(3) = 2*a(2)+5 = 22+5 = 27
a(4) = 2*a(3)+5 = 54+5 = 59
a(5) = 2*a(4)+5 = 118+5 = 123<br>
Look for the pattern to deduce the formula for the n-th term.<br>
The numbers are approximately doubling each time; so compare the sequence to appropriate powers of 2:<br><pre>
  this sequence:   3   11   27   59  123
  powers of 2:     8   16   32   64  128
                   ---------------------
  differences:     5    5    5    5    5</pre><br>
The n-th term in the sequence is 5 less than 2 to the power (n+2):<br>
{{{t(n) = 2^(n+2)-5}}}<br>
So the 50th term is {{{2^52+5}}}, which is a huge number....<br>