IB Mathematics Analysis and Approaches Question Type 4: Finding Sum of First n Terms Given First Term and Common Difference Exercises

Derive the general formula for the sum $S_n$ of the first $n$ terms of an arithmetic sequence in terms of $u_1$, $d$, and $n$.

Find the sum of the first 6 terms of an arithmetic sequence with first term $u_1=3$ and common difference $d=8$.

Calculate the sum of the first 20 terms of an arithmetic sequence with $u_1=15$ and $d=5$.

Find the sum of the first 8 terms of an arithmetic sequence where $u_1=12$ and $d=-3$.

Determine the sum of the first $5$ terms of an arithmetic progression with initial term $7$ and common difference $7$.

Calculate the sum of the first 10 terms of an arithmetic progression with $u_1=5$ and $d=2$.

Find the sum of the first 20 terms of an arithmetic sequence with $u_1=9$ and $d=-2$.

Calculate the sum of the first 15 terms of an arithmetic sequence with $u_1=-4$ and $d=6$.

Determine the sum of the first 25 terms of an arithmetic progression where $u_1=100$ and $d=-4$.

Find the sum of the first 12 terms of an arithmetic sequence where $u_1=2$ and $d=0.5$.

Determine the sum of the first 9 terms of an arithmetic sequence with $u_1=\frac{1}{3}$ and $d=\frac{1}{3}$.

Calculate the sum of the first 40 terms of an arithmetic progression where $u_1=4.2$ and $d=1.8$.