Multiple choice

The sum of how many terms of the series $6+12+18+24+.....$ is $1800$?

  1. $16$
  2. $24$
  3. $20$
  4. $18$
  5. $22$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is an arithmetic progression with a=6, d=6. Sum = n/2 * (2a + (n-1)d) = 1800. n/2 * (12 + (n-1)6) = 1800. n * (6 + 3n - 3) = 1800. 3n^2 + 3n - 1800 = 0. n^2 + n - 600 = 0. (n+25)(n-24) = 0. n = 24.

AI explanation

Using the arithmetic progression sum formula n divided by 2 multiplied by the quantity 2a plus the quantity n minus 1 times d, we set the sum equal to 1800 with the first term as 6 and the common difference as 6. This gives 1800 equals n times 6 plus 3 times the quantity n minus 1, which simplifies to 1800 equals 3n squared plus 3n, and further to n squared plus n minus 600 equals 0. Factoring this gives n equals 24, so the result is 24.

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