Question

1+4+7+.....+100=?va rog sa má ajutati

Answer 1

    
[tex]\displaystyle 1+4+7+.....+100=? \\ \\ n = \frac{100-1}{3}+1 = \frac{99}{3}+1 =33+1 = 34\;de ~termeni. \\ \\ 1+4+7+.....+100= \frac{34(100+1)}{2}=17 \times 101 = 17 * 101= \boxed{1717}[/tex]

Answer 2

$\displaystyle 1+4+7+...+100 \\ \\ 100=1+(n-1) \times 3 \\ \\ 100=1+3n-3 \\ \\ 3n=100-1+3 \\ \\ 3n=102 \\ \\ n= \frac{102}{3} \\ \\ n=34$

$\displaystyle S_{34}= \frac{2+33 \times 3}{2} \times 34 \\ \\ S_{34}= \frac{2+99}{2} \times 34 \\ \\ S_{34}= \frac{101}{2} \times 34 \\ \\ S_{34}=101 \times 17\\ \\ S_{34}=1717$