The first three terms of arithmetic progression {an} are A- 1, 4, 2a, and the tolerance is d.

a 1= a- 1，a2=4，a3=2a，

Then d = 4-a+ 1 = 2a-4,

∴3a=9,a=3,a 1= a- 1 = 3- 1 = 2，a 1=2

d=4-a+ 1=4-2=2，

The general formula of (1){ an}: an = a1+(n-1) d = 2+2 (n-1) = 2n.

an=2n

(2)Sk=2550，

∫Sn = na 1+n(n- 1)d/2 = 2k+2k(k- 1)/2

∴2k+k？ -k=2550，k？ +k-2550=0，(k+5 1)(k-50)=0，

∴k=50，k =-5 1。

Test: ak= a50= 100, sk = s50 = (2+100) × 50/2 = 2550, correct.