# Converges and Diverges

#### hahaitssara

Arithmetic word problem

The first row of seating in section H of the Concert Area has 7 seats. In all, there are 25 rows of seats in section H, each row containing 2 seats more than the row preceding it. How many seats are in section H?

My attempt:

it is an arithmetic problem i guess.
a1=7
a1+(n-1)d
7+(25-1)2=55 seats
is this how you do this problem?

Last edited:

#### Plato

MHF Helper
The first row of seating in section H of the Concert Area has 7 seats. In all, there are 25 rows of seats in section H, each row containing 2 seats more than the row preceding it. How many seats ?
$$\displaystyle \sum\limits_{k = 0}^{24} {\left( {7 + 2k} \right)} = ?$$

#### hahaitssara

Converge

im sorry i really do not understand what that means!

#### Plato

MHF Helper
im sorry i really do not understand what that means!
I am sorry that I misunderstood.
I thought you were in a pre-calculus course.
Do you realize that you posted this in the pre-calculus forum?

#### hahaitssara

I am in pre calculus, however I do not understand the symbol of E we never learned that. I don't know what your trying to explain! Please help!

#### Plato

MHF Helper
I am in pre calculus, however I do not understand the symbol of E we never learned that. I don't know what your trying to explain! Please help!
Are you really in a pre-calculus course in which the idea of summation is not considered?
It is very hard to believe that any pre-calculus course would not discuss the notation $$\displaystyle \sum\limits_{k = 0}^{24} {a_k }$$.

I truly hope that your course will serve you future needs.

#### hahaitssara

I dont see how it makes any difference to you. This is a pre-calculus question and I need help. I see that I am not getting it from you!

#### Danneedshelp

I dont see how it makes any difference to you. This is a pre-calculus question and I need help. I see that I am not getting it from you!
The first row has 7 seats, since k=0 zero when you are at the first row. If you move up to the second row k=1, so there are 7+2(1)=9 seats. If you move up to the third row k=2, so there are 7+2(2)=11 seats. You can continue this for k=3,...,24 (since there are 25 rows and we consider the first row to be row 0). The notation Plato posted tells you to add up each one of these terms. So,

$$\displaystyle \sum_{k=0}^{24}7+2k=7+9+11+13+...$$, where $$\displaystyle k$$ is the index of the summation, 0 is the lower bound (the initial value of k) and 24 is the upper bound (the final value of k). Thus, you begin at k=0 and add the following terms up until you get to k=24.

Hopefully that clears things up.

hahaitssara