The first 4 terms of an arithmetic sequence are {3,10,17,24}... 1)Find an expression for the nth term 2) is 150 in the sequence?

PART 1Step 1: Common difference 10 - 3 = 717-10 = 724-17 = 7so common difference is 7 Step 2: find the 0th term0th term is the term before the first term which is3-7 = -4Step 3: Use general formula for arithmetic sequencesIn general An = (common difference)*n - [0th term]nth term = (7)*n -[4]Step 4: Test the answer to make sure it is correct7(0) - 4 = 47(1) - 4 = 107(2) - 4 = 17etc...
PART 2We will assume that 150 is in the sequencewhich means that :7n - 4 = 150(solve for n)7n = 154n = 22so yes, 150 is then 22nd term in the sequence