Question

o ciągu geometrycznym (an) wiemy, że a2=8 i a3=4. Oblicz a10 i S10.

Answer 1

a2=8

a3=4

q=a3/a2

q=4/8

q=1/2

a2=a1*q

8=a1*1/2/*2

16=a1

a1=16

a10=a1*q^(n-1); ^do potęgi

a10=16*(1/2)^9

a10=16*1/512

a10=1/32

                1-q^n

S10=-a1*---------;

               1-q

               1-(1/1024)

S10=16*--------

              1-1/2

 

S10=16*[(-1023)/1024]*2

S10=-1023/32

s10=-31 i31/32

Answer 2

a3=a2*q

4=8*q

q=1/2

a10=a2*8*q

a10=8*(1/2)do potęgi 8

a108/256=1/36

a1=16

s10=16*(1-1/1024)/(1-1/2)=32736/1024=31,96875