Question

3. Cati termeni are suma 4+6+8+10+...+202
A.202 termeni B.198 termeni C.200 termeni D.100 termeni
4.Rezultatul calculului 4+6+8+10+...+202 este nr:
A.10300 B.20600 C.40400 D.20200

Answer 1

A 202 termeni cred si cred ca D.20200

Answer 2

$\displaystyle 4+6+8+10+...+202 \\ \\ 202=4+(n-1) \times 2 \\ \\ 202=4+2n-2 \\ \\ 2n=202-4+2 \\ \\ 2n=200 \\ \\ n= \frac{200}{2} \\ \\ n=100~termeni$

$\displaystyle S_{100}= \frac{8+99 \times 2}{2} \times 100 \\ \\ S_{100}= \frac{8+198}{2} \times 100 \\ \\ S_{100}= \frac{206}{2} \times 100 \\ \\ S_{100}= 103 \times 100 \\ \\ S_{100}=10300 \leftarrow rezultatul$