We will use the equation f(n+1) = -10*f(n) to generate successive terms after this first term. --------------- Second term f(n+1) = -10*f(n) f(1+1) = -10*f(1) ... plug in n = 1 f(2) = -10*f(1) f(2) = -10*1 ... replace f(1) with 1 (works because f(1) = 1) f(2) = -10
Put another way, the second term is -10 times the first term second term = -10*(first term) second term = -10*(1) second term = -10 --------------- Third term f(n+1) = -10*f(n) f(2+1) = -10*f(2) ... replace n with 2 f(3) = -10*f(2) f(3) = -10*(-10) ... replace f(2) with -10 (works because f(2) = -10) f(3) = 100 which is the answer we want
In other words, the third term is -10 times the second term third term = -10*(second term) third term = -10*(-10) third term = 100 --------------- Summary of the three terms f(1) = 1 f(2) = -10 f(3) = 100 Each term is found by multiplying the previous term by -10
