The sequence is given by the formula an = 53 / (n + 1). How many members of this sequence are more than 6?

1. Since the formula for the n-th term of the progression is given, and the condition is given, we write the inequality:
53 / (n + 1)> 6;
53> 6 * (n + 1);
53> 6n + 6;
6n <47;
n <47/6;
n <7 5/6;
2. It can be written as follows, given that n is a natural number:
n ∈ [1; 7].
In this range, n can be equal to:
1, 2, 3, 4, 5, 6, 7. There are 7 values in total.
That is, 7 members of the progression are more than 6.
Answer: 7 members of this sequence are more than six.