Question Type 5: Finding sum of first n terms and common difference given first term and last term Exercises

Find the sum of the first $20$ terms, $S_{20}$.

In the arithmetic progression where $u_1 = 3$ and $u_6 = 43$, determine how many terms are required so that the sum of the first $n$ terms exceeds 1000.

Given the arithmetic progression with $u_1=3$ and $u_6=43$, find the sum of the terms from $u_5$ to $u_{15}$.

An arithmetic sequence has first term $3$ and sixth term $43$. Find the common difference and hence express the sum of the first $n$ terms, $S_n$, in the form $an^2+bn$.

In the arithmetic progression with $u_1=3$ and $u_6=43$, find the sum of the first $10$ terms, $S_{10}$.

Given $u_1=3$ and $u_6=43$, find the 20th term and the sum of the first 20 terms.

In the arithmetic sequence with $u_1 = 3$ and $u_6 = 43$, derive an expression for the sum of the first $n$ terms, $S_n$, in terms of $n$.