Quick questions on Arithmetic and Geometric Sequences - TCE Mathematics Applications (Tasmania)

For an arithmetic sequence with first term $a$ and common difference $d$: $$t_n = a + (n-1)d$$

The sum of the first $n$ terms is written $S_n$.

A common exam task reverses the question: instead of finding a term from its position, you are given a term value and must find which position it is. For an arithmetic sequence, set $t_n = a + (n-1)d$ equal to the known value and solve the linear equation for $n$. For a geometric sequence you solve $a r^{\,n-1} = \text{value}$, which usually needs logarithms or a guess-and-check on the calculator. Always check that $n$ comes out as a whole number, because a non-integer means the value is not actually a term of the sequence.