In a sequence where each term is the square of its position, what is the sum of

₹0.0

Question: In a sequence where each term is the square of its position, what is the sum of the first 4 terms? (2023)

Options:

Correct Answer: 30

Exam Year: 2023

Solution:

The first four terms are 1^2, 2^2, 3^2, 4^2 which are 1, 4, 9, 16. Their sum is 30.

In a sequence where each term is the square of its position, what is the sum of the first 4 terms? (2023)

In a sequence where each term is the square of its position, what is the sum of the first 4 terms? (2023)

Step 1: Identify the position of each term in the sequence. The first four positions are 1, 2, 3, and 4.
Step 2: Calculate the square of each position. For position 1, the square is 1^2 = 1. For position 2, the square is 2^2 = 4. For position 3, the square is 3^2 = 9. For position 4, the square is 4^2 = 16.
Step 3: List the squares you calculated: 1, 4, 9, and 16.
Step 4: Add the squares together: 1 + 4 + 9 + 16.
Step 5: Calculate the sum: 1 + 4 = 5, then 5 + 9 = 14, and finally 14 + 16 = 30.

Sequences and Series – Understanding how to generate terms in a sequence based on a defined rule, in this case, squaring the position.
Summation – Calculating the total of a set of numbers, specifically the first four terms of the sequence.