Arithmetic progression problem

**mastermin346** · Jan 8th 2010, 05:02 PM

How many terms at least of the arithmetic progression 1,4,7,10,.............are needed to give a sum greater than 590,starting from the first term of the arithmetic progression?

please help me

**skeeter** · Jan 8th 2010, 05:29 PM

Originally Posted by mastermin346

How many terms at least of the arithmetic progression 1,4,7,10,.............are needed to give a sum greater than 590,starting from the first term of the arithmetic progression?

$S_n = \frac{n}{2}(t_1 + t_n) > 590<br />$

where $t_n = t_1 + d(n-1)$

solve for the least value of $n$ that makes the sum greater than 590

**mastermin346** · Jan 8th 2010, 08:41 PM

Originally Posted by skeeter

$S_n = \frac{n}{2}(t_1 + t_n) > 590<br />$

where $t_n = t_1 + d(n-1)$

solve for the least value of $n$ that makes the sum greater than 590

how?? i dont know how to do..

**Prove It** · Jan 8th 2010, 09:14 PM

Do as you have been instructed.

$S_n = \frac{n}{2}(t_1 + t_n)$

$= \frac{n}{2}[t_1 + t_1 + (n - 1)d]$

$= \frac{n}{2}[2t_1 + (n - 1)d]$

You should be able to see that $t_1 = 1$ and $d = 3$

So $S_n = \frac{n}{2}[2(1) + 3(n - 1)]$

$= \frac{n}{2}(2 + 3n - 3)$

$= \frac{n}{2}(3n - 1)$

$= \frac{3n^2}{2} - \frac{n}{2}$ .

You know that $S_n > 590$

So $\frac{3n^2}{2} - \frac{n}{2} > 590$

Solve for $n$ .

Choose the first whole value of $n$ that is greater than what you found...

**mastermin346** · Jan 8th 2010, 10:00 PM

Originally Posted by Prove It

Do as you have been instructed.

$S_n = \frac{n}{2}(t_1 + t_n)$

$= \frac{n}{2}[t_1 + t_1 + (n - 1)d]$

$= \frac{n}{2}[2t_1 + (n - 1)d]$

You should be able to see that $t_1 = 1$ and $d = 3$

So $S_n = \frac{n}{2}[2(1) + 3(n - 1)]$

$= \frac{n}{2}(2 + 3n - 3)$

$= \frac{n}{2}(3n - 1)$

$= \frac{3n^2}{2} - \frac{n}{2}$ .

You know that $S_n > 590$

So $\frac{3n^2}{2} - \frac{n}{2} > 590$

Solve for $n$ .

Choose the first whole value of $n$ that is greater than what you found...

what do you mean by "Choose the first whole value of

that is greater than what you found"???

**mr fantastic** · Jan 8th 2010, 10:23 PM

Originally Posted by mastermin346

what do you mean by "Choose the first whole value of

that is greater than what you found"???

You have been given almost the entire solution. Your job is to read and process what you've been told and then finish off the problem.

Solve $\frac{3n^2}{2} - \frac{n}{2} = 590 \Rightarrow \frac{3n^2}{2} - \frac{n}{2} - 590 = 0$ for n. Choose the value of n that is positive and satisfies $\frac{3n^2}{2} - \frac{n}{2} - 590 \geq 0$ .

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