CAT 2021 Progression Question (Medium)

Question

Natural numbers are divided into groups as follows:

Group 1: (1)
Group 2: (2, 3, 4)
Group 3: (5, 6, 7, 8, 9)
Group 4: (10 … 16)
…and so on, where the k‑th group contains (2k–1) numbers.
What is the sum of the numbers in the 15th group?

Accepted Answer

Step 1 Number of Numbers in Groups up to k-1 Group k has 2k 1 numbers. Total numbers before Group k is sum_ i 1 k-1 2i - 1 This is the sum of the first k 1 odd numbers 1 3 5 dots 2 k-1 -1 k-1 2 because the sum of first odd numbers is Thus, the last number in Group k 1 is . --- Step 2 First and Last

CAT 2021

Quantitative

Progression

Medium

Natural numbers are divided into groups as follows:

Group 1: (1)

Group 2: (2, 3, 4)

Group 3: (5, 6, 7, 8, 9)

Group 4: (10 … 16)
…and so on, where the k‑th group contains (2k–1) numbers.
What is the sum of the numbers in the 15th group?

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