Question

Find the sum of the first 38 terms: 9/2,5,11/2,6,13/2

Answer 1

Ths sum of the first 38 terms is
`(1,045)/(2)=522.5`

Explanation:

Arithmetic Sequences

They are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

`a_n=a_1+(n-1)r`

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

The sum of n terms of the sequence is

`S_n=(n)/(2)( a_1 + a_n)`

The common difference is found by subtracting two consecutive terms:

`r=a_(n+1)-a_n`

Using the first two terms:

`r=a_2-a_1=5-(9)/(2)=(1)/(2)`

Now we find the term n=38

`\displaystyle a_(38)=(9)/(2)+(38-1)(1)/(2)`

`\displaystyle a_(38)=(9)/(2)+(37)/(2)=(46)/(2)=23`

The sum is:

`\displaystyle S_(38)=(38)/(2)( (9)/(2) + 23)`

`\displaystyle S_(38)=19( (9+46)/(2))`

`\displaystyle S_(38)=19( (55)/(2))= (1,045)/(2)=522.5`

Ths sum of the first 38 terms is
`\mathbf{(1,045)/(2)=522.5}`