Calculate the sum

Question

Calculate the sum: 3+ 7+ 11+ ......+ 399

Answer 1

a_n = a₁ + (n - 1)d

399 = 3 + (n - 1)4

396 = 4n - 4

400 = 4n

100 = n

 

S_n = (n/2)(a₁ + a_n)

S₁₀₀ = (100/2)(3 + 399)

S₁₀₀ = (50)(402)

S₁₀₀ = 20100

Answer 2

The pattern is that the next tern increases by 4 

 

the term equation is 3+ 4* n , where n is the number of the term

 

So the 0th term is 3

the 1st terns is 3+4*1 = 7

the 2 nd term is 3+4 *2 = 11

 

we need to sum the terms from 3 to 399 and we need to know which is the n for 399:

 

we do it by solving equation 3 +4 *n =399 which give us that 399 is term # 99

 

Now we use the summation notation summing all the members of sequence from 0 to 99 :

 

Sum from 0 to 99 (3+4n) = 20100.

 

Hope it helps.