Current location - Training Enrollment Network - Mathematics courses - Mathematics problems in senior one. Important process.
Mathematics problems in senior one. Important process.
1. In the geometric series an, what is a5*a6*a7=3, a6*a7*a8=24, a7*a8*a9?

Solution: (a? Answer? Answer? )/(a? Answer? Answer? )=a? /a? =a? q? /a? =q? =24/3=8,∴q=2.

Answer? Answer? Answer? =(a? )? q? =3, so a? =(3/8)^( 1/3)=(? 3)/2

∴a? Answer? Answer? =(a? q? )(a? q? )(a? q? )=(a? )? (q? )=(3/8)×2? =3×2? =3×64= 192.

2. If the sum of the first five terms of a geometric series is equal to 10 and the sum of the first ten terms is equal to 50, what is the sum of its first 15 terms?

Solution: S/S? =q? +1=5, then q? =4

s? =a? (q? - 1)/(q- 1)=a? (4- 1)/[4^( 1/5)- 1]=3a? /[4^( 1/5)- 1]= 10

So a? = 10[4^( 1/5)- 1]/3

∴s={( 10/3)[4^( 1/5)- 1](q- 1)}/(q- 1)={( 10/3)[4^( 1/5)- 1](64- 1)/[4^( 1/5)- 1]=( 10/3)×63=2 10