已知数列{an}满足a1=1,a2=a(a>0),数列{bn}=an*an+bn=an*an+1 若{an}是等差数列,且b3=12,求a及an通项⑵若{an}是等比数列,求{bn}的前n项的和sn

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已知数列{an}满足a1=1,a2=a(a>0),数列{bn}=an*an+bn=an*an+1 若{an}是等差数列,且b3=12,求a及an通项⑵若{an}是等比数列,求{bn}的前n项的和sn
已知数列{an}满足a1=1,a2=a(a>0),数列{bn}=an*an+
bn=an*an+1 若{an}是等差数列,且b3=12,求a及an通项⑵若{an}是等比数列,求{bn}的前n项的和sn

已知数列{an}满足a1=1,a2=a(a>0),数列{bn}=an*an+bn=an*an+1 若{an}是等差数列,且b3=12,求a及an通项⑵若{an}是等比数列,求{bn}的前n项的和sn
(1){an}是等差数列,a1=1,a2=a(a>0),
an=1+(n-1)(a-1)
a3=2a-1,a4=3a-2
b3=a3*a4=(2a-1)(3a-2)=12
a=2,或-5/6(舍去)
所以a=2,an=n
(2){an}是等比数列,a1=1,a2=a(a>0),
a3=a^2,a4=a^3
b3=a3*a4=a^5=12
a=5次根号12
an=(5次根号12)^(n-1)
bn=an*an+1=(5次根号12)^(n-1)(5次根号12)^n=(5次根号12)^(2n-1)
{bn}的前n项的和sn=[1-(5次根号12)^(2n+1)]/[1-(5次根号12)^2