an+ 1=3an+ 1-2an
Is it ... or not
An +2
=
3an+ 1
-
2an
If it is.
Solution:
⑴、
Let bn=an+ 1.
-
Ann, it is easy to know that b 1=a2-a 1=2,
By condition: an+2
=
3an+ 1
-
2an
get
(An +2
-
An+1)
=
2(an+ 1
-
Ann)
Namely bn+ 1
=
2 billion pounds
And b 1=2≠0.
So the series (an+ 1
-
Ann)
Is a geometric series, the common ratio is 2, and the first term is 2.
⑵、
Bn = b 1q (n- 1) = 2 n, and the sum of the first n terms sn = 2 (2 n- 1).
So:
An+1
-
One; one
=
2^n
One; one
-
an- 1
=
2^(n- 1)
……
a3
-
Aortic second sound
=
2^2
Aortic second sound
-
a 1
=
2
Add up all the formulas to get it.
An+1
-
a 1
=
2^n
+
2^(n- 1)
+……+
2^2
+
2
=bn
+
bn- 1
+……+
b2
+
b 1
=
tin
=2(2^n- 1)
And a 1= 1.
therefore
An+1
=
2(2^n
-
1)
+ 1
=
2^(n+ 1)
-
1
One; one
=
2^n
-
1
The second question uses dislocation addition. Then use the sum of the first n terms of geometric series to solve it.