tmua.me Extreme Set C Paper 1 · Question 1

tmua.me papers

tmua.me Extreme Set C Paper 1 · Q1

Paper 1Sequences & seriesPowers & logarithmsNumber & counting

The positive integers occurring in either of the sequences

1,4,7,10,\ldots \qquad\text{and}\qquad 1,2,4,8,\ldots

are combined into one increasing sequence $a_1,a_2,a_3,\ldots$ . An integer occurring in both original sequences is listed only once.

What is the sum of all the indices $n$ satisfying

1\leq n\leq99\qquad\text{and}\qquad a_{n+1}-a_n=1\,?

4

58

64

68

166

170

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.