Question

Se considera sirul :1,6,11,16,21,.....,4021,....
a) Aflati cati termeni are sirul pana la 4021 insclusiv .
b) Aflati termenul de pe locul 208 .
c) Calculati suma :S=1+6+11+16+....+4021.

Answer 1

    
$a) \\ n = numarul\;de\;termeni. \\ n= \frac{4021-1}{5} +1=\frac{4020}{5} +1=804+1=\boxed{805\;termeni} \\ \\ b) \\ n=208 \\ t = termenul \;de \;pe \;locul \;208. \\ n=\frac{k-1}{5} +1 \\ 208=\frac{k-1}{5} +1 \\ 208-1=\frac{k-1}{5} \\ k-1=207 \cdot 5 \\ k-1=1035 \\ k = 1035+1 =\boxed{1036}$

$c) \\ S = \frac{805 \cdot (4021+1)}{2} =\frac{805 \cdot 4022}{2} =805 \cdot 2011=\boxed{1618855}$