first we need to find the common ratio by dividing the second term by the first term. 36/120 = 3/10
an = a1 * r^(n-1) n = term to find = 5 a1 = first term = 120 r = common ratio = 3/10 now we sub and solve a5 = 120 * 3/10^(5 - 1) a5 = 120 * 3/10^4 a5 = 120 * .0081 a5 = 0.972 <=== fifth term
or we could have just done this......since we multiply by 3/10 to find the next number... a3 = 10.8......10.8 * 3/10 = 3.24 <== 4th term 3.24 * 3/10 = 0.972 <== fifth term
The formula for geometric sequence is an = a1 r^(n-1) where r is the geometric factor and n is an interger. In the sequence given, r is equal to 3/10. In this case, an = 120* (3/10)^(n-1). Solving for a5, a5 = 120* (3/10)^(5-1) = 0.972
