Inanarithmeticseries,thetermsoftheseriesareequallyspreadout.Forexample,in1+5+9+13+17,consecutivetermsare4parts.Ifthefirstterminanartihmeticseriesis3,thelasttermis136,andthesumis1,390,whatarethefist3terms?A.3,10,

Question

In an arithmetic series,the terms of the series are equally spread out.For example,in 1+5+9+13+17,consecutive terms are 4 parts.If the first term in an artihmetic series is 3,the last term is 136,and the sum is 1,390,what are the fist 3 terms?
A.3,10,17
B.3,23,43
C.3,36 1/3,70
D.3,69 1/2,136
E.3,139,1,251
请解释下怎么算,公式是啥?

Answer 1

等差数列问题.公式：
和＝（首项＋末项）×项数÷2
首项=2*和÷项数-末项
末项=2*和÷项数-首项
末项=首项+（项数-1）×公差
题中项数=1390*2/(3+136)=20
公差=（136-3）/(20-1)=7
所以前三项为3,10,17