# Arithmetic Progression (AP)

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

• Can you place your efforts into the question, so we can see where you are struggling? – Kevin May 15 '18 at 10:03
• This seems like insufficient information. – Piyush Divyanakar May 15 '18 at 10:04
• Indeed. For example: $71, 71, 71, \ldots, 71$. – StackTD May 15 '18 at 10:10
• The question has no sequence given. It is from a question paper. Other questions under the same question are: calculate the value of the 9th and the 15th terms, calculate the sum of the first five terms – Mercy Flicker May 15 '18 at 10:13
• quite alright I can solve the first equations for the last four which comes to be 4a+6d = 284. Now how to get another equation to solve it using simultaneous method that's where I fail – Mercy Flicker May 15 '18 at 10:15

$284$ 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.
From your Problem we get $$a_1+14d+a_1+15d+a_1+16d+a_1+17d=284$$ an equation in two unknowns.
• So how can I solve for a and d? – Mercy Flicker May 15 '18 at 10:16
• Are $$a_1,d$$ integer numbers? – Dr. Sonnhard Graubner May 15 '18 at 10:20