Question

consider the arithmetic sequences is 5,7,9 a)what is first term b)what number will you get if 4 is added to the sum of first 3 terms of this sequence c) prove that the sum of any number of term of this sequence starting from the first added to give a perfect square​

Answer 1

Answer:

The first row of seating in an outdoor amphitheater contains 26 seats, the second row contains 28 seats, the third row contains 30 seats, and so on. If there are 18 rows, what is the total seating capacity of the theater?

Figure 9.2

Roman Theater (Wikipedia)

Solution:

Begin by finding a formula that gives the number of seats in any row. Here the number of seats in each row forms a sequence:

26,28,30,…

Note that the difference between any two successive terms is 2. The sequence is an arithmetic progression where a1=26 and d=2.

an====a1+(n−1)d26+(n−1)⋅226+2n−22n+24

Therefore, the number of seats in each row is given by an=2n+24. To calculate the total seating capacity of the 18 rows we need to calculate the 18th partial sum. To do this we need the 1st and the 18th terms:

a1a18==262(18)+24=60

Use this to calculate the 18th partial sum as follows:

SnS18=====n(a1+an)218⋅(a1+a18)218(26+60)29(86)774

Answer: There are 774 seats total.