7. The 17th term of an AP is 22, and the sum of the first 17 terms is 102. Find

the 1st term and the common difference.

ANSwer: a1=10;d=2

can you please help me understand the working

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- Apr 20th 2013, 09:50 AMBenja303Arthimetic progression help
7. The 17th term of an AP is 22, and the sum of the first 17 terms is 102. Find

the 1st term and the common difference.

ANSwer: a1=10;d=2

can you please help me understand the working - Apr 20th 2013, 10:07 AMPlatoRe: Arthimetic progression help

Every term of the AP is $\displaystyle a_n=a_1+(n-1)d$.

So $\displaystyle a_{17}=a_1+16d=22.$ and $\displaystyle \sum\limits_{k = 1}^{17} {{a_k}} = \sum\limits_{k = 1}^{17} {\left( {{a_1} + (k - 1)d} \right)} = 17{a_1} + \frac{{16 \cdot 17}}{2}d = ?$

Now it is your turn. - Apr 20th 2013, 10:08 AMMarkFLRe: Arthimetic progression help
The nth term is:

$\displaystyle a_n=a_1+(n-1)d$

The sum of the first n terms is:

$\displaystyle S_n=\frac{n(a_1+a_n)}{2}$

Use the second equation to find $\displaystyle a_1$, then use the first to find $\displaystyle d$. What do you find? - Apr 20th 2013, 10:51 AMBenja303Re: Arthimetic progression help
Ohhh thanks mark. I was doing it was N/2 X the rest. I see . The 2 divides the entire thing. cool. Nice whip by the way.

- Apr 20th 2013, 11:39 AMMarkFLRe: Arthimetic progression help