已知等差数列:1,4,7,10,.求a10和s10等于

Question

已知等差数列:1,4,7,10,.求a10和s10等于

Answer 1

设等差数列通项式为 an = a1 + (n-1) * q 其中 a1 = 1 ; n 为项数,q是公差,
将 a2 = 4 ; n=2 代入上式,有 4 ＝ 1 + （2－1）* q 解得,q = 3
所以,等差数列的通项公式为 an = 1 + 3 (n-1) = 3 n - 2
将 n = 10 代入,有 a10 = 30 - 2 = 28
由高斯定律,sn = (a1 + an) * n / 2 将 a1 =1 ; a10 = 28 ; n = 10 代入高斯定律：得
s10 = (1 + 28) * 10 / 2 = 145