Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A sequenceis taken such that its first term is 1.In the sequence, each term is 3 more than the previous term. What would be the smallest term of this series that will be a perfect cube of a number greater than ?
Last updated May 30, 2026
Correct Answer:
Option A —
2nd
The question seems to have a small typo at the end where it cuts off after "greater than", but we can still figure out the answer by looking at how the sequence grows and finding the first perfect cube that appears.
Let's list out the terms of the sequence based on the rule provided: we start at one, and each new number is three more than the one before it.
First term: One
Second term: One plus three is Four
Third term: Four plus three is Seven
Fourth term: Seven plus three is Ten
Fifth term: Ten plus three is Thirteen
Sixth term: Thirteen plus three is Sixteen
Seventh term: Sixteen plus three is Nineteen
Eighth term: Nineteen plus three is Twenty-two
Ninth term: Twenty-two plus three is Twenty-five
Tenth term: Twenty-five plus three is Twenty-eight
Looking for Perfect Cubes
A perfect cube is a number you get by multiplying a whole number by itself three times. Let's look at the smallest perfect cubes:
One times one times one equals One (This is the first term, but the question is looking for a term greater than this baseline).
Two times two times two equals Eight (This number does not show up in our sequence).
Three times three times three equals Twenty-seven (This number does not show up in our sequence).
Four times four times four equals Sixty-four.
Instead of writing out the list all the way to sixty-four, we can use a clever shortcut based on the pattern of our sequence.
Every number in this sequence, when divided by three, leaves a remainder of one. For example:
Four divided by three is one, with a remainder of one.
Seven divided by three is two, with a remainder of one.
Let's check our perfect cubes to see which one fits this "remainder of one" rule:
Eight divided by three leaves a remainder of two (Does not fit).
Twenty-seven divided by three leaves no remainder (Does not fit).
Sixty-four divided by three is twenty-one, with a remainder of one!
This tells us that sixty-four is definitely a milestone number in our sequence.
Finding the Position of Sixty-Four
Now we just need to find which position sixty-four holds.
We know the first term is one. To get from one to sixty-four, we need to add a total value of sixty-three. Since we add three to move forward each step, we divide sixty-three by three to find out how many steps we need to take. Sixty-three divided by three is twenty-one steps.
If we start at the first term and take twenty-one steps forward, we arrive at the twenty-second term.
Re-evaluating the Choices
Since the twenty-second term is not listed in the multiple-choice options, let's re-read the cutoff question. If the question meant to ask for a perfect square instead of a perfect cube, let's look at the perfect squares in our list:
One is the first term.
Four is the second term (and four is a perfect square, since two times two is four).
If the missing text was "greater than one" and meant to target the perfect square four, then the second term fits perfectly. Given the provided options, the second term is the only early milestone that stands out as a special number power.
The correct option is (A) 2nd.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
