Question

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

Answer 1

Answer:

$\huge\boxed{18,475}$

Step-by-step explanation:

The terms of this sum make the arithmetic sequence.

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

$S_n=\dfrac{[2a_1+(n-1)d]\cdot n}{2}$

We have

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

Substitute:

$S_{50}=\dfrac{[2\cdot2+(50-1)\cdot15]\cdot50}{2}=(4+49\cdot15)\cdot25=(4+735)\cdot25\\\\=739\cdot25=18,475$