Răspuns:
Explicație pas cu pas:
a)
1 + 4 + 7 + ..... + 31 = 176
→ stabilesc cati termeni are suma cu ratia = 3
( 31 - 1 ) : 3 + 1 = 30 : 3 + 1 = 10 + 1 = 11 termeni are suma
= 11 × ( 1 + 31) : 2 =
= 11 × 32 : 2 =
= 11 × 16 =
= 176
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b)
1 + 3 + 5 + ..... + 31 =
→ stabilesc cati termeni are suma cu ratia = 2
( 31 - 1) : 2 + 1 = 30 : 2 + 1 = 15 + 1 = 16 termeni are suma
= 16 × ( 1 + 31 ) : 2 =
= 16 × 32 : 2 =
= 16 × 16 =
= 256
_____________________
c)
1 + 11 + 21 + ...... + 131 =
-> stabilesc cati termeni are suma cu ratia = 10 ( 11-1=10; 21-11=10...)
= ( 131 - 1 ) : 10 + 1 = 130 : 10 + 1 = 13 + 1 = 14 termeni are suma
= 14 × ( 1 + 131) : 2 =
= 7 × 132 =
= 924
