Current location - Training Enrollment Network - Mathematics courses - High school math sequence problem! ~ ~ Waiting for the answer online
High school math sequence problem! ~ ~ Waiting for the answer online
1. In arithmetic progression, it is known that A 1+A2 = 4 and A3+A4 = 12, then a5+a6=__20__?

a 1+a2=2a 1+d=4

a3+a4=2a 1+5d= 12

4d=8,d=2,a 1= 1

a5+a6 = 2a 1+9d = 2+ 18 = 20

What is the sum of integers between 2.50 and 350 with the last digit of 1?

(5 1+34 1)*30= 1028 1

3. In a positive geometric progression, if a4a5=6, a1AAA7A8 equals _ _?

a 1a2a7a8=(a4a5)^2=36

4. Given the numbers 2, 5 and 8 in the series, what is the number of the series with twice the number 5?

2 root number 5= root number 20

20=2+(n- 1)3=3n- 1

n=7

5. If A, B and C are geometric series, what is the number of alternating current between the image of function y=ax +bx+c and the X axis?

A, b and c do geometric series.

So b 2 = AC

b^2-4ac=b^2-4b^2=-3b^2<; 0

So the intersection is 0.

6. In arithmetic progression, if the sum of the first five items is S5=20, then a3=___?

S5=5a 1+ 10d=20,a 1+2d=4

a3=a 1+2d=4

7. The first n terms of geometric series are marked as Sn. If S4 = 2 and S8 = 6, then S 12 = _ _?

s4/s8=( 1-q^4)/( 1-q^8)= 1/( 1-q^4)= 1/3

q^4=2

q^ 12=8

s4/s 12=( 1-q^4)/( 1-q^ 12)=( 1-2)/( 1-8)= 1/7

2/S 12= 1/7

S 12= 14

8. If the series is arithmetic progression, the first item is a1>; 0,a 2007+a 2008 & gt; 0, a2007 a2008 & lt0, then what is the largest natural number that makes the first n terms and Sn > 0 hold?

a2007 a2008 & lt0

So in 2008,

a2007 & gt-a 2008 & gt; 0

So s 4015 >; 0

9. It is known that in geometric series, a3=3, a 10=384, then the general term an=____?

a 1+2d=3

a 1+9d=384

7d=38 1

d=38 1/7

a 1=-74 1/7

an =-74 1/7+(n- 1)38 1/7

10. in arithmetic progression, a 1 and a2 are two roots of the equation X -3x-5=0, then A5+A8 = _ _ _?

x^2-3x-5=0

a 1,2=(3 √29)/2

When a 1=(3+√29)/2, d=√29, a5+a8=3+ 12√29.

When a 1=(3-√29)/2, d=-√29, a5+a8=3- 12√29.

1 1. In arithmetic progression, A 1+A2+A3 =-24, A 18+A 19+A20 = 78, so the first 20 items and S20 = _ _?

a2=a 1+d=-8

a 19 = a 1+ 18d = 26

d=2,a 1=- 10

S20=-200+ 190*2= 180

12. The first n items of the sequence are recorded as Sn. If Sn=n squared -3n+ 1, then an = _ _ _?

a 1=- 1

an=n^2-3n+ 1-(n- 1)^2+3(n- 1)- 1=2n-4

13. in arithmetic progression, the tolerance d is not equal to 0, and A 1, A3 and A9 are in geometric series, so (a3+a6+a9)/(a4+a7+a10) = _ _?

(a 1+2d)^2=a 1(a 1+8d)

d=a 1

(a3+a6+a9)/(a4+a7+a 10)

=(3a 1+ 15d)/(3a 1+ 18d)

= 18d/2 1d

= 18/2 1

fast

Tired

Give it to me! ! !