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 $d = 1.8$.