<PRE><B>Question 1203626</B>
(5 + 8 + 11 + 14 + . . . + 299 + 302) = 

This is an arithmetic sequence because the common difference between each consecutive term is constant  The sum of an arithmetic sequence  is given by the formula:

Sn= (n/2) * [2a + (n-1)d]

n is the number of terms.
a is the first term.  -------------a= 5
d is the common difference ------- d=3
First we have  to find the number of terms in the sequence ,n

To find n, we use the formula for the nth term of an arithmetic sequence:
nth term = a + (n-1)d

Plug values

302 = 5 + (n-1) * 3

302 - 5 = (n-1) * 3
297 = (n-1) * 3

Divide  by 3

99 = n - 1

So n = 100

There are 100 terms in this serquence. n=100

Now, put these values into the sum formula:

Sn = (100/2) * [2 * 5 + (100-1) * 3]
Sn = (50) * [10 + 99 * 3]
Sn = 50 * (10 + 297)
Sn = 50 * 307
Sum = 15,350

Therefore, the sum of the given terms  is 15,350.





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