The sum of first 60 positive integers divisible by 6 is : 14650 16440 14640 14604
The correct answer and explanation is:
Correct Answer: 11070
Let us calculate the sum of the first 60 positive integers divisible by 6.
Any number divisible by 6 can be expressed as:
6 × n, where n is a positive integer.
So, the first 60 positive integers divisible by 6 are:
6, 12, 18, 24, …, up to the 60th term.
This forms an arithmetic sequence, where:
- First term (a) = 6
- Common difference (d) = 6
- Number of terms (n) = 60
The formula for the sum (Sₙ) of the first n terms of an arithmetic sequence is:
Sₙ = (n/2) × (2a + (n – 1)d)
Plugging in the values:
S₆₀ = (60/2) × (2 × 6 + (60 – 1) × 6)
= 30 × (12 + 59 × 6)
= 30 × (12 + 354)
= 30 × 366
= 10980
Alternatively, use the simpler sum formula:
Sₙ = n/2 × (first term + last term)
Find the 60th term:
T₆₀ = a + (n – 1)d = 6 + (60 – 1) × 6 = 6 + 354 = 360
Then:
S₆₀ = (60/2) × (6 + 360) = 30 × 366 = 10980
Now compare with the answer choices you provided:
- 14650
- 16440
- 14640
- 14604
None of these match the correct value. So the correct sum is not listed among your choices. The accurate value is:
Answer: 10980
Explanation Summary
To find the sum of a sequence of numbers divisible by 6, treat it as an arithmetic sequence. Use either the standard sum formula or the version with first and last terms. Always verify the last term by generating it using the arithmetic rule. The calculated sum of the first 60 multiples of 6 is 10980.