Question

The nth term of a sequence is n2+20a)What is the first three terms of the sequence?

b.many terms in the sequence are less than 50?

Answer 1

`a_n=n^2+20\\\\a)\\a_1=1^2+20=1+20=21\\a_2=2^2+20=4+20=24\\a_3=3^2+20=9+20=29\\\\Answer:\ 21;\ 24;\ 29\\\\b)\\n^2+20 < 50\ \ \ |-20\\\\n^2 < 30\to n < √(30)\ \wedge\ n\in\mathbb{N^+}\to\ n\in\{1;\ 2;\ 3;\ 4;\ 5\}\\\\Answer:\ 5\ terms`