Question

What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47+ ...?​

Answer 1

`\huge\boxed{18,475}`

Explanation:

The terms of this sum make the arithmetic sequence.

The fomula of a sum of n terms of an arithmetic sequence:

`S_n=([2a_1+(n-1)d]\cdot n)/(2)`

We have

`a_1=2\\d=17-2=32-12=47-32=15\\n=50`

Substitute:

`S_(50)=([2\cdot2+(50-1)\cdot15]\cdot50)/(2)=(4+49\cdot15)\cdot25=(4+735)\cdot25\\\\=739\cdot25=18,475`