nth term and equations

a ppt is here

it might be helpful to link an nth term rule/relationship to a linear equation
solving an equation to find the value of 'n' that has a given number of sticks in the sequence
i.e. given what the nth term value is, obtain the sequence rule and then use this to work out what n is in this sequence to give the required value

with an intention to relate the diagrams to the solution steps
and seeing how this links with the steps involved with solving an equation

all nth term rules involve 'bunches' (the multiplier) with an adjustment (add/subtract a constant number)   
you can identify these 'bunches' by seeing how much the sequence grows each time                                                             

for these you take some sticks away first to obtain the 'bunches'

for these you add some sticks first to obtain the 'bunches'