Sequence

2,7,13,18,22 …

 

General Equation

 

t_n = 2 + (n - 1) (5)

 

t_n = 2 + (5n) - 5

 

t_n= 5n - 3

 

Finding t_{50}

 

t_{50} = 2 + (50-1) (5)

 

t_{50} = 2 + 49 (5)

 

t_{50} = 2 + 245

 

t_{50} = 247

 

Sum of 50 terms

 

S_{50} = \frac{50}{2} (2 + 247)

 

S_{50} = 25 (249)

 

S_{50} = 6225