The sum of the numbers 3, 6, 9, 12, … up to the 20th term is :
600
1260
630
960
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2022
The first term (a) is 3.
The common difference (d) is 6 – 3 = 3 (or 9 – 6 = 3, etc.).
We need to find the sum of the first 20 terms (n = 20).
The formula for the sum of the first n terms of an AP is Sn = n/2 * [2a + (n-1)d].
Substituting the values:
S20 = 20/2 * [2 * 3 + (20 – 1) * 3]
S20 = 10 * [6 + 19 * 3]
S20 = 10 * [6 + 57]
S20 = 10 * 63
S20 = 630
– Identify the first term (a) and the common difference (d).
– Use the formula for the sum of the first n terms of an AP: Sn = n/2 * [2a + (n-1)d].
The sum is 3 * (1 + 2 + 3 + … + 20).
The sum of the first n natural numbers is n(n+1)/2.
So, the sum of 1 to 20 is 20(20+1)/2 = 20 * 21 / 2 = 10 * 21 = 210.
The sum of the sequence is 3 * 210 = 630.
This confirms the result obtained using the AP sum formula.