Question

7. a) Determine the sum of all the multiples
of 4 between 1 and 999.
b) What is the sum of the multiples of 6
between 6 and 999?

Answer 1

Sn = n/2 (a1 + an)

n = the number of terms (in this case, the number of multiples of 4 between 1 and 999)
a1 = first term
an = last term
Sn = the sum of all the terms

Answer 2

Do you know how to find the total number of multiples of 4 between 1 and 999

Answer 3

Well... if not, here it is
an = a1 + (n - 1)d

Answer 4

so for a) it's a multiple of 4, so your d=4. An=999 and a1=4. Substitute it in and solve, you get n=249. Now that you know what n is, plug that in the Summation formula above and solve. Sn would be 124,500

Answer 5

for b) everything is the same, only d this time equals 6, solve using the same procedure

Answer 6

I didn't get 124,500 for part (a). Instead, I got 124,873.5. Here's what I did: Sn= 249 (4+999)

Answer 7

What did I do wrong?

Answer 8

here's the problem, 999 is not the right number to plug in (since it's not a multiple of 4)

Answer 9

Oh right. Then do I manually find the last number closest to 999 which is a multiple of 4?

Answer 10

yup :)

Answer 11

I see. Thank you.

Answer 12

Got it!

Answer 13

Is the answer to part b 82,190?

Answer 14

Sorry, 82,170?

Answer 15

My book says it's 82,665

Answer 16

Here's what I did: Sn = 165/2 (6+990)

Answer 17

an is 996...

Answer 18

make sure you pay extra careful attention to that lol, because you made the same mistake in both part a and b