Find the infinite geometric sum of 80 + 10 +1.25 + to 5 decimal places past the decimal point.

first term.

a= 80

second term. a2=10

so Common ratio r=a2/a =10/80=1/8=0.125

checking for the validity of common ratio.

a2×r=10×1/8=10×0.125=1.25 =a3= Third term.

Hence it is true.

Now 4th Term =1.25/8=0.15625

It can be observed that 4TH term Has digit that is 5 places past the decimal point.

Hence, 0.15625 is the terminating number as per the question.

So the required sum is.

S=a+a2+a3+a4

->S=80+10+1.25+0.15625

->S= 91.40625

Hope it helps...

Regards,

Leukonov/Olegion.

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

contact me if you have any questions you are welcome.