Question:

$S_n = 1^3 + 2^3 + 3^3 + ... + n^3$ and $T_n = 1 + 2 + 3 + 4 ......n$

Updated On: Jun 12, 2024
  • $S_n = T^3_n$
  • $S_n = T_{n^2}$
  • $S_n = T_{n}^2$
  • $S_n = T_{n}^3$
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The Correct Option is C

Solution and Explanation

Put n = 2 and verify the options.
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Concepts Used:

Arithmetic Progression

Arithmetic Progression (AP) is a mathematical series in which the difference between any two subsequent numbers is a fixed value.

For example, the natural number sequence 1, 2, 3, 4, 5, 6,... is an AP because the difference between two consecutive terms (say 1 and 2) is equal to one (2 -1). Even when dealing with odd and even numbers, the common difference between two consecutive words will be equal to 2.

In simpler words, an arithmetic progression is a collection of integers where each term is resulted by adding a fixed number to the preceding term apart from the first term.

For eg:- 4,6,8,10,12,14,16

We can notice Arithmetic Progression in our day-to-day lives too, for eg:- the number of days in a week, stacking chairs, etc.

Read More: Sum of First N Terms of an AP