Question

Find the sum of all multiple 3 between 5 and 64

Answer 1

Answer: ∑=690

Explanation:

Let's use the formulas for an arithmetic progression:

`a_1=6 \ \ \ \ \ a_n=63\ \ \ \ d=3\\a_n=a_1+(n-1)d\\63=6+(n-1)3\\63=6+3n-3\\63=3+3n\\63-3=3+3n-3\\60=3n\\`

Divide both parts of the equation by 3:

`20=n`

Thus,

`\displaystyle\\\sum=(a_1+a_n)/(2) n\\\\\sum=(6+63)/(2)20 \\\\\sum=(69*20)/(2) \\\\\sum=69*10\\\\\sum=690`

Answer 2

690

Explanation:

The multiples of 3 between 5 and 64 are 6+9+12+15+18+21+24+27+30+33+36+39+42+45+48+51+54+57+60+63 which gives you 690.

Hope this helps, have a good day! :D