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
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.
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?