Question

Am nevoie urgent de ajutor! Dau coroana si inima!
1) b6=39; b16=59; b1=? , r=?

2)b1=8; r=3; a100=? , s100=?

3) b1=3; q=4; b9=?

4)b1=1/4; q=2; b8=?

5)b5=16; b1=1; q=?

Answer 1

Răspuns:

1. Dupa notatii pare o progresie aritmetica (trebuie scris enuntul intreg, nu trebuie sa banuim noi asta)!!!

Putem folosi mai multe căi

bn-bm=(n-m) *r sau

bn=b1+(n-1)*r

bm=b1+(m-1)*r

b16-b6=10*r

59-39=10*r

r=2

b6=b1+5r

b1=39-5*2=29

2.

b100=b1+99*r=8+99*3=8+297=305

Suma primilor 100 termeni se poate scrie

S=b1+b2+.... +b100=b1+(b1+r) +(b1+2r)+....b1+99r= 100*b1+(1+2+3+...99)*r=100*b1+ r* 99*100/2=100*8+3*50*99=800+3*50*99

3.

Daca e vorba de progresie geometrica

b1=3

q=4

bn=b1 * q^(n-1)

b9=b1*q^8=3*4^8

4.

b8=b1* q^7=1/4 * 2^7=1/4 *128=32

5.

b5=b1 *q^4

16=1 * q^4

2^4=q^4

2=q