Question

A)Determinati:6+11+16+21+... +506. B)Efectuați:4+9+14+19+...+1004.​

Answer 1

Răspuns:

Explicație pas cu pas:

a ) 6 + 11 + 16 + 21 + ..... + 506 =

-> stabilesc cati termeni are suma cu ratia = 5 (11-6=5; 16-11=5...)

( 506 - 6) : 5 + 1 = 500 : 5 + 1 = 101 termeni are suma

= 101 × ( 6 + 506) : 2 =

= 101 × 512 : 2 =

= 101 × 256 =

= 25 856

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b)   4 + 9 + 14 + 19 + ....... + 1004 =

-> stabilesc cati termeni are suma cu ratia = 5 (9-4=5;  14-9=5;    ......)

( 1004 - 4 ) : 5 + 1 = 1000 : 5 + 1 = 201 termeni are suma

= 201 × ( 4 + 1004 ) : 2

= 201 × 1008 : 2 =

= 201 × 504 =

= 101 304

Answer 2

a)

6 = 6 + 5·0

11 = 6 + 5·1

16 = 6 + 5·2

21 = 6 + 5·3

.

.

.

506 = 6 +5·100

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S = 101·6 + 5(1+2+3+ ... + 100)=606+5·(100·101)/2 =606 +5·50·101=

=606 +50·505 =606 +25250 =25 856