Term and sum of an arithmetic progression

Text

An arithmetic progression has first term $a_1=7$ and common difference $d=4$.

• (a) Compute the twentieth term $a_{20}$.
• (b) Compute the sum of the first twenty terms $S_{20}$.

Solution

(a) The general term is $a_n=a_1+(n-1)d$, so $a_{20}=7+(20-1)\cdot 4=7+76=83.$ (b) The sum of the first $n$ terms is $S_n=n\cdot\dfrac{a_1+a_n}{2}$: $S_{20}=20\cdot\frac{7+83}{2}=20\cdot 45=900.$ $\boxed{\,a_{20}=83,\quad S_{20}=900\,}$