The sequence a₁, a₂, a₃, ... is an arithmetic sequence with common difference d>0. The term a₆, a₁₀, and a₁₇ form a geometric sequence. If a₁ = 1, find the sum of first 2022 terms in a sequence?
What I have tried: I have tried to make many sequences with numbers (trial and error), but after many failed attempts, not a single sequence fit the restrictions.
Hint: $a_n=1+(n-1)d$ and $(1+5d)(1+16d)=(1+9d)^{2}$. Expand the square . You can determine the exact value of $d$ from this so you know what $a_n$ is.