Question Type 3: Working with arithmetic sequences algebraically Exercises

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 $k$.

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 $100$.

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 $u_n>100$.

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 $a$.

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