Given that the general term formula of the sequence {an} is an = (- 1) n + 1 (3n-2), write the 5th and 100th term of the sequence? Like the title, 2, f (x) = AX2 + B, f (1) = - 1, f (2) = 8 Find the value of a, B and f (5) 3. If log ZX = 3, then x =?

Given that the general term formula of the sequence {an} is an = (- 1) n + 1 (3n-2), write the 5th and 100th term of the sequence? Like the title, 2, f (x) = AX2 + B, f (1) = - 1, f (2) = 8 Find the value of a, B and f (5) 3. If log ZX = 3, then x =?

A: 13, - 198

General term formula of increasing sequence

an=a1+d(d>0)

The difference of sequence is increasing. How to write such a general term formula?
Like 33, 35, 39, 45, 53, 63 How to find the general term formula for such a sequence?

a2-a1=b
a3-a2=2b
a4-a3=3b
.
an-an-1=(n-1)b
Add
an-a1=(n-1)b+(n-1)(n-2)b/2
=n(n-1)b/2
an=a1+n(n-1)b/2
This is the second order arithmetic sequence n quadratic

Increasing sequence formula
1, 3, 6, 10, 15. Find the sum of this sequence and what is the nth term?
For this kind of non arithmetic sequence, how to calculate Sn and an?

a2-a1=2
a3-a2=3
a4-a3=4
a5-a4=5
……
an-an-1=n
An-a1 = 2 + 3 + +n=(n-1)(2+n)/2
an=(n-1)(2+n)/2+1
The recurrence relation can be found out, and then the general term can be obtained by accumulating, multiplying, splitting the term and constructing a new arithmetic or proportional sequence;
The sum can be obtained by formula, grouping, splitting term,