Question Type 3: Working with arithmetic sequences algebraically Bootcamps

For the arithmetic sequence defined by $a_n=4n-1$, determine its first term and common difference.

In an arithmetic sequence, the 7th term is $25$ and the 15th term is $49$. Find the first term and the common difference.

For the arithmetic progression defined by $u_1=3$ and $u_6=43$, find the smallest integer $n$ such that $u_n>100$.

The sequences $a_n=2+3(n-1)$ and $b_n=k+5(n-1)$ have the same 11th term, and this term equals $32$. Find $k$.

In an arithmetic sequence, the 8th term is twice the 3rd term. Express the common difference $d$ in terms of the first term $a$.

Three consecutive terms of an arithmetic sequence are $a$, $ab$, and $a+b$. Express $b$ in terms of $a$.

Consider the arithmetic sequences $u_n=12+4(n-1)$ and $v_m=20+2(m-1)$. List all terms common to both sequences that are less than $100$.