a2+a4=20

a 1*q+a 1*q^3=20

The formula a 1 * q 2 = 8 is divided by 1/q+q=5/2 q=2 or q= 1/2 geometric progression.

q=2 a 1=2 an=2^n

2.

( 1)an=2a(n- 1)+2^n- 1

n=4 a4=2a3+2^4- 1 a3=33

n = 3 a3=2a2+2^3- 1 a2 = 13

n = 2 a2=2a 1+2^2- 1 a2 = 5

(2) (a1+p)/2 (a2+p)/4 (a3+p)/8 is arithmetic progression.

( 13+p)/2 =(5+p)/2+(33+p)/8 p =- 1

Tolerance d= 1

(3)

(an- 1)/2^n=(a 1- 1)/2+(n- 1)d=n+ 1

an=(n+ 1)*2^n+ 1

sn=(2*2^ 1+ 1)+(3*2^2+ 1)+(4*2^3+ 1)+……+((n+ 1)*2^n+ 1)

=2*2^ 1+3*2^2+4*2^3+……+((n+ 1)*2^n+n

Let bn = 2 * 21+3 * 2+4 * 2 3+...+((n+1) * 2n.

2bn = 2 * 22+3 * 23+4 * 24+...+((n+1) * 2 (n+1) subtraction.

-bn=2*2^ 1+(2^2+2^3+2^4+……+2^n)-((n+ 1)*2^(n+ 1)

=2^(n+ 1)-((n+ 1)*2^(n+ 1)

Bn=n*2^(n+ 1)

Sn=Bn+n=n*2^(n+ 1)+n