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

Using $u_1=3$ and $u_6=43$, find the sum of the first $20$ terms, $S_{20}$.

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.

An arithmetic progression 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 $an^2+bn$.

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

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

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 $1000$.