If the sum of the first n terms of an Arithmetic Progression is equal to $n^2 + 3n$

Question

If the sum of the first n terms of an Arithmetic Progression is equal to $n^2 + 3n$ then the first term of the Arithmetic Progression is enter image description here I tried to solve this question by putting sum of of $n^th$ term of an Arithmetic Progression that is $(n÷2)(2a+(n-1)d)$= $n^2+3n$ but won't end up with an answer.please help me.

You appear to be confusing "arithmetic sequence" with "geometric" sequence. Your $n^th$ is for a geometric sequence.. The general form for an arithmetic sequence is $a+ nh$. — user247327, Jun 21 '19 at 16:05
@user247327: OP was giving formula for sum of arithmetic sequence — J. W. Tanner, Jun 21 '19 at 16:08

score 3 · Accepted Answer · answered Jun 21 '19 at 15:55

3

Taking $n=1$ we see that $S_1=a_1=4$.

answered Jun 21 '19 at 15:55

lulu

70,402

Dr. Sonnhard Graubner · Answer 2 · 2019-06-21T16:22:18.223

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From your formula we get $$\frac{n(2a_1+(n-1)d)}{2}=n^2+3n$$ for $$n\neq 0$$ we get $$2a_1=2n+6-(n-1)d$$ so...?

edited Jun 21 '19 at 16:22

answered Jun 21 '19 at 15:52

Dr. Sonnhard Graubner

95,283

You left out ÷2 from OP's formula – J. W. Tanner Jun 21 '19 at 16:19
1

Thank you!! Corrected! – Dr. Sonnhard Graubner Jun 21 '19 at 16:22
The question is asking about the value of a by this method I got only the value of a in terms of n which will not solve my question as I can't put this value anywhere to solve the question. – Ankit Kumar Jun 21 '19 at 16:36
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Ok, then take $$n=1$$, then you will get $$2a_1=8$$ – Dr. Sonnhard Graubner Jun 21 '19 at 16:37

If the sum of the first n terms of an Arithmetic Progression is equal to $n^2 + 3n$

2 Answers2