Question

se considera suma S=5+9+13+...+397. Sa se determine numărul termenilor din suma S. Sa se calculeze suma S.

Answer 1

5=4×0+5
9=4×1+5
13=4×2+5
397=4×97+9
S=(4×0+5)+(4×1+5)+(4×2+5)....(4×97+9)+9+9+9
S=0+4+8....388| ÷4
0+1+2....97
S=4×(1+2+3+...97)+9×98
4×[(97×98)÷2]+882=19894

Answer 2

S = 5+9+13+...+397

5=1+4

9=5+4

13=9+4

397=393+ 4

………………………….

Ratia este 4

Sn =  a1×n+r×[n(n-1)/2]=5×397+4×397 ×398/2=5×397+4×397 ×398/2=317997