S9=9a+36d=72 a+4d=8
a2+a4+a9 = a+d+a+3d+a+8d = 3a+ 12d = 3(a+4d)= 3 * 8 = 24
Second, the common ratio in geometric series is 4, and the sum of the first three terms is 2 1. What is the general formula?
a 1 = a a2 = 4a a3 = 16a a 1+a2+a3 = 2 1a = 2 1a = 1
an=4^(n- 1)
3. It is known that abcd is a geometric series, the vertex coordinate of the function y=x squared -2x+8 is (b, c), and what is ad?
The vertex of y = x 2-2x+8 = (x- 1) 2+7 is calculated as (1, 7) b= 1 c=7. q=c/d=7, so a =1/7d =
ad=7
4. arithmetic progression a 1+a2+a3+a4+a5+a6=27, what is a3? (Why? )
a 1+a2+a3+a4+a5+a6 = a3-2d+a3-d+a3+a3+d+a3+2d+a3+3d = 6 a3+3d = 27
I can't figure it out
5. The sum of the first few terms in the geometric series is Sn, 4a 1, 2a2, a3 becomes arithmetic progression. If a 1= 1, then S4=?
sn=a 1( 1-q^n)/( 1-q)
a 1 = 1 4a 1 = 4 a2 = q 2 a2 = 2q a3=q^2
2q-4=q^2-2q q=2
s4=( 1-2^4)/( 1-2)= 15
6. arithmetic progression a3=7, a5+a7=26, and the sum of the preceding items of an is Sn. What about an and Sn?
a5=a3+2d a7=a3+4d
a5+a7=2a3+6d=26
6d=26-2a3=26-2*7= 12
D=2, so a 1=a3-2d=7-4=3.
an=3+(n- 1)*2=2n+ 1
Sn=(3+2n+ 1)n/2=n(n+2)