SOLUTION: Consider the following sequence of numbers: 2;4;2;7;2;10;2;13;... a) Calculate the sum of the 50 terms of sequence.

Algebra ->  Sequences-and-series -> SOLUTION: Consider the following sequence of numbers: 2;4;2;7;2;10;2;13;... a) Calculate the sum of the 50 terms of sequence.      Log On


   

Question 626885: Consider the following sequence of numbers:
2;4;2;7;2;10;2;13;...
a) Calculate the sum of the 50 terms of sequence.
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
t%5B1%5D=2
t%5B2%5D=4
t%5B3%5D=2
t%5B4%5D=7
t%5B5%5D=2
t%5B6%5D=10
t%5B7%5D=2
t%5B8%5D=13

Thus, for n=1,2,3,...,etc. we can write t%282n-1%29=2 and t%282n%29=4%2B3%28n-1%29

To find sum up to first 50 terms
sum%28+t%28i%29%2C+i=1%2C+50+%29
= sum%28+t%282k%29+%2B+t%282k+-+1%29%2C+k=1%2C+25+%29
= sum%28+4%2B3%28k-1%29+%2B+2%2C+k=1%2C+25+%29
= sum%28+3%28k%2B1%29%2C+k=1%2C+25+%29
= 3%2Asum%28+k%2B1%2C+k=1%2C+25+%29
= 3%2A%28%2825%2A%2825%2B1%29%2F2%29%2B25%29
= 3%2A%2825%2A13%2B25%29
= 3%2A25%2A14=1050