The arithmetic progression is given by the formula an = 6n-306. Indicate the largest number, starting from which

The arithmetic progression is given by the formula an = 6n-306. Indicate the largest number, starting from which all members of the progression: a) greater than -12. b) are positive

1. The condition of the problem is the formula of the arithmetic progression аn = 6 n – 306.

And so you can determine the largest number, after which all members will be greater than -12, if we compose the inequality

6 n – 306> -12, whence 6 n> 294 and, accordingly, n> 49.

2. To find the number of a member of the progression, after which all subsequent ones will be positive, we again compose the inequality

6 n – 306> 0;

6n> 306;

n> 51.

Answer: Starting from number 50, all members of the arithmetic progression are greater than -12, and starting from number 52 they are all positive.