Arithmetic Progression (AP)

Question

An arithmetic progression (AP) has 18 terms. If the sum of the last four terms of the AP is 284. calculate the first term and the common difference

Answer 1

From your Problem we get $$a_1+14d+a_1+15d+a_1+16d+a_1+17d=284$$ an equation in two unknowns.

Answer 2

$284$ is a rectangle with sides $4$ and $71$. Notice, if you subtract a multiple of $3$ from $71$ to get the size of the first partition, your difference in $AP$ will become a multiple of $2$ accordingly.

$68+70+72+74=65+69+73+77=62+68+74+80 =\ ...\ = 284$

Since your first term of $AP$ is dependent on the common difference, your problem has many solutions.