NBT NBT Mathematics: Sequences, Series and Patterns 5

Question 1

What is the sum of all integers from 1 to 100?

Accepted Answer

5050

Answer

Sₙ = n(n+1)/2 = 100(101)/2 = 5050.

Question 2

A sequence has Tₙ = 5 × 2ⁿ⁻¹. Which statement is true?

Accepted Answer

It is geometric with r = 2

Answer

The formula Tₙ = arⁿ⁻¹ with a = 5 and r = 2 defines a geometric sequence.

Question 3

If ∑ₙ₌₁⁸ aₙ = 96 and each term is equal, what is each term?

Accepted Answer

12

Answer

If all 8 terms are equal, each term = 96 ÷ 8 = 12.

Question 4

The 4th term of an arithmetic sequence is 25 and the 9th term is 50. What is the common difference?

Accepted Answer

5

Answer

T₉ − T₄ = 5d = 25 → d = 5.

Question 5

A pattern of squares: 1st figure has 1 square, 2nd has 5, 3rd has 13, 4th has 25. What is the general term?

Accepted Answer

Tₙ = 2n² − 2n + 1

Answer

Tₙ = 2n²−2n+1 gives T₁=1, T₂=5, T₃=13, T₄=25, matching the pattern exactly.

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