已知各项均不等的等差数列An的前5项和为S5=35,A1+1,A3+1,A7+1成等比数列.求An的通项公式

设等差数列An的公差为dA3=A1+2d A7=A1+6dS5=A1+4d=35①∵A1+1,A3+1,A7+1成等比数列∴(A3+1)²=(A1+1)(A7+1)(A1+2d+1)²=(A1+1)(A1+6d+1)整理得A1-2d=-1②联立①②解得A1=11 d=6An=A1+(n-1)d=11+6(n-1)