Saturday, April 29, 2017

Find the sum of the first 75 terms of the arithmetic sequence that starts 5,8,11,ldots



Find the sum of the first 75 terms of the arithmetic sequence that starts 5,8,11,




The answer is 8700.



I found a formula to be 3x+2.
So the 1st term is
3(1)+2=5


2nd term
3(2)+2=8

3rd term
3(3)+2=11


And so on to the 75th term
3(75)+2=227

I did not get the right answer? What did I do wrong? Please help?


Answer



u1=5


u2=8=5+3

u3=11=5+2.3

u75=5+74.3=227



S=5+8+11+...+224+227



S=227+224+...8+5

by sum
2S=232+232+...232=232.75



S=116.75=8700


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