Question

Find the missing term in the series given below 3,16,83,?,2107,10544

Answer 1

The next term would be 83. The logic behind this is that, the difference of each consecutive pair of terms is in an increasing A.P. as illustrated below:

pair 1: 11–3= 8 = d1

pair 2: 23–11= 12 =d2, d2–d1=4

pair 3: 39–23= 16 =d3, d3-d2=4

pair 4: 59–39= 20 = d4, d4-d3=4, which means d5-d4=4

THIS implies the next difference d5= d4+4, which in turn implies the next term in the series is 59+d5= 59 + d4 + 4 =59 + 20 + 4 =83.