what is the 50th term in the following arithmetic number pattern: 10, 13, 16,...?

For the arithmetic number pattern :
The first term, a = 10
The common difference, d = 13 - 10 = 16 - 13 = 3

The 50 term
= a + (50 - 1)d
= 10 + (50 - 1) × 3
= 10 + 49 × 3
= 10 + 147
= 157

Since 3 is added to each number, and 3 numbers are already given, you are looking for the next 47th term. Counting from 16...
16 + (3 x 47)= 157

10, 13, 16, 19, ...
an = 3n + 7
a50 = 157

157

10 + 49 * 3

nth term = 3n + 7
So 50th term= 3(50) + 7 = 157

10 + 49 * 3

141