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

Mathematics

1 answer:

Alex3 years ago

3 0

Answer:

$\huge\boxed{18,475}$

Step-by-step explanation:

The terms of this sum make the arithmetic sequence.

The fomula of a sum of <em>n</em> 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:

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

You might be interested in

Jeff can paint 28 sqaure feet every 30 mintues angela can paint 50 square feet every hour who can paint faster,and by how many s

Gnesinka [82]

Answer:

6/1 square feet per hour. Jeff can paint faster.

Step-by-step explanation:

So, to get Jeff's square feet to 60 minutes, you do 30x2= 60. So, you do that to 28. 28x2= 56. 56/1 is greater then 50/1. So 56-50= 6. Jeff can paint 6 square feet per hour, greater than Angela.

Hope this helped!

4 0

4 years ago

A telemarketing company calls telephone numbers chosen at random. It finds that 70% of calls arc not completed (the party does n

saw5 [17]

Answer:

We conclude that the 8 % of calls result in a sale.

We conclude that the 5.3% of sales are made to women.

Step-by-step explanation:

We know that 70% of calls arc not completed (the party does not answer or refuses to talk), that 20% result in talking to a woman, and that 10% result in talking to a man. After that point, 30% of the women and 20% of the men actually buy something.

We calculate what percentage of calls result in a sale, and we get:

$p=\frac{20}{100}\cdot \frac{30}{100}+\frac{10}{100}\cdot \frac{20}{100}\\\\p=\frac{6}{100}+\frac{2}{100}\\\\p=\frac{8}{100}$