The Geometric Term Formula Let's use an example to show where the formula comes from. 2, 8, 32, 128, 512, ... The first term a is 2.      The common ratio r is 4 t1 = 2 t2 = 2 x 41 = 8 t3 = 2 x 42 = 32 t4 = 2 x 43 = 128 t5 = 2 x 4? = 512   What is the missing number? Can you see that it is always one less than the term number n? t5 = 2 x 44 = 512 The formula for any term in this sequence must be: tn = 2 x 4n-1 Generalizing this for any geometric sequence, the formula would be: tn = a x rn-1 This is the Geometric Sequence Term Formula. Back