The Arithmetic Term Formula Let's use an example to show where the formula comes from. 5, 9, 13, 17, 21,... The first term a is 5.      The common difference d is 4 t1 = 5 t2 = 5 + 1 x 4 = 9 t3 = 5 + 2 x 4 = 13 t4 = 5 + 3 x 4 = 17 t5 = 5 + ? x 4 = 21   What is the missing number? Can you see that it is always one less than the term number n? t5 = 5 + 4 x 4 = 21 The formula for any term in this sequence must be: tn = 5 + (n-1) x 4 Generalizing this for any arithmetic sequence, the formula would be: tn = a + (n-1) x d This is the Arithmetic Sequence Term Formula. Back