Can you help me understand how Arithmetic sequences work?

Let us look at an example first, imagine there is the following sequence:2, 4, 6, 8, 9, 10...Let the difference be constant d, in this case d = 2If I were to ask what would be the value of the 10th number in the sequence, how would you calculate it?a₁= 2a₂ = 4so if you just keep on adding a₁₀ = 18This is easy if the numbers are small, however what if I were to ask for the 100th number or even 10000th number?To make it easier we need to come up with a formula that can calculate it let's substitute the numbers with variables. Let's take the previous example.a₁= 2 ;a₂ = 4 ; a₂ - a₁= 2 = d ;if we rearrange this equation,a₂= a₁ + d ;a₃= a₂ + d = a₁ + d + d ;a₄= a₃ + d = a₁ + d + d +d ;
do you see a trend, its always one added d a_n = a₁ + (n-1)*dSo let us say I would want to know what given that d = 2 and the initial value a₁ = 2 and I want to find the 20th value, if we use the equationa_n = a₁ + (n-1)*da₂₀ = 2 + (20 -1)2 = 2 +192 = 2 + 38 = 40