Question

已知等差数列〔an〕的前4项和为10，且a2 ，a3 ，a7成等比数列?（1）试求数列〔an〕的通项公式an?（2）...

已知等差数列〔an〕的前4项和为10，且a2 ，a3 ，a7成等比数列?（1）试求数列〔an〕的通项公式an?（2）设bn=2^an，求数列〔bn〕的前n项和Sn

Answer 1

(1) a+(a+d)+(a+2d)+(a+3d) = 10
2a + 3d =5
(a+2d)^2 = (a+d)*(a+6d)
a =-2, d=3
an = -2+(n-1)*3 = 3n - 5
(2) bn = 2^(3n-5)
sn = 2^(-2) [ 1- 2^(3n)] / (1-2^3) = (2^(3n)-1)/28