Given that the sum of the first n terms of the sequence (an) is Sn = 2an-4n + 1, the general term formula of the sequence is obtained RT

Given that the sum of the first n terms of the sequence (an) is Sn = 2an-4n + 1, the general term formula of the sequence is obtained RT

The formula an = SN-S (n-1) n is greater than or equal to 2
have to
an=（2an-4n+1）-（2an-1 - 4n + 5)
=2an-2an-1 - 4
The equation is transformed by shifting terms
an+4=2（an-1 +4）
So the sequence (an + 4) is an equal ratio sequence with (A2 + 4) as the first term and 2 as the common ratio
therefore
An + 4 = (A2 + 4) * 2 is n-2 power
therefore
An = (A2 + 4) * 2 gives n-2 power - 4
When n = 1, A1 = 3 is obtained from Sn = 2an-4n + 1, that is, A1 = 2a1-3
A1 + A2 = 2a2-7 leads to A2 = 10. When A1 and A2 are brought into the general formula, the above formula is satisfied when n = 1
The general formula is
An = 14 * 2, then n-2 power - 4 N belongs to natural number
Or write it
An = 7 * 2 ^ (n-1) - 4 N belongs to natural number

If the arithmetic sequence {an} satisfies that A4 equals 7 and A7 equals 1, then an equals 1

a4=a1+3d=7
a7=a1+6d=1
a1=13 d=-2
an=a1+(n-1)d=13-2(n-1)=-2n+15

In the arithmetic sequence, it is known that A4 = 10, a7 = 19, find A1 and tolerance D and an

A7-A4=3d
3d=19-10=9
d=3
A1=A7-6d
=19-18=1
An=A1+(n-1)d
=1+3(n-1)
=3n-2