document.write( "Question 1168283: what is the first five terms and 50th term of this sequence.
\n" ); document.write( "An=2a n-1 + 5 and a1=3 \n" ); document.write( "

Algebra.Com's Answer #792903 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Follow the instructions to find the first 5 terms recursively:

\n" ); document.write( "a(1) = 3
\n" ); document.write( "a(2) = 2*a(1)+5 = 6+5 = 11
\n" ); document.write( "a(3) = 2*a(2)+5 = 22+5 = 27
\n" ); document.write( "a(4) = 2*a(3)+5 = 54+5 = 59
\n" ); document.write( "a(5) = 2*a(4)+5 = 118+5 = 123

\n" ); document.write( "Look for the pattern to deduce the formula for the n-th term.

\n" ); document.write( "The numbers are approximately doubling each time; so compare the sequence to appropriate powers of 2:

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document.write( "  this sequence:   3   11   27   59  123\r\n" );
document.write( "  powers of 2:     8   16   32   64  128\r\n" );
document.write( "                   ---------------------\r\n" );
document.write( "  differences:     5    5    5    5    5

\n" ); document.write( "The n-th term in the sequence is 5 less than 2 to the power (n+2):

\n" ); document.write( " $\"t%28n%29+=+2%5E%28n%2B2%29-5\"$

\n" ); document.write( "So the 50th term is $\"2%5E52%2B5\"$ , which is a huge number....

\n" ); document.write( " \n" ); document.write( "

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