Can you find the rule describing the nth term of the sequence of square numbers? Class 9

Can you find the rule describing the n^th term of the sequence of square numbers? Class 9

Question 1.

Can you find the rule describing the n^th term of the sequence of square numbers? Class 9

Answer:

The sequence of square numbers is: 1, 4, 9, 16, 25,...

Each term is the square of its position.

∴ u_n = n², is the rule describing the nth term of the sequence of square number.

Question 2.

Consider the expression t_n = 3n - 7.

i. Find its first, second, third, 12^th, 18^th and 50^th terms. Class 9

ii. Which term of the sequence is 332?

iii. Is 557 a term of this sequence? Why or why not?

Answer:

Given: t_n = 3n - 7

i. To find the first, second, third, 12^th, 18^th and 50^th terms, substitute n = 1, 2, 3, 12, 18 and 50 in the given expression:

t₁ = 3(1) - 7 =-4

t₂ = 3(2) - 7 = - 1

t₃ = 3(3) -7 = 2

t₁₂ = 3(12) - 7 = 36 - 7 = 29

t₁₈ = 3(18) - 7 = 54 - 7 = 47

t₅₀ = 3(50) - 7 = 150 - 7 = 143

∴ The terms are: -4, - 1, 2, 29, 47, 143.

ii. Let n^th term of sequence be 332

i. e., t_n = 332

∴ 3n - 7 = 332

∴ 3n = 339

∴ n = 113

∴ 113^th term of sequence is 332.

iii. Let n^th term of sequence be 557.

∴ t_n = 557

∴ 3n - 7 = 557

∴ 3n = 564

∴ M = 188

∵ 188 is a natural number.

∴ 188^th term of sequence is 557.

If the value of n is not a natural number, then 557 is not a term of the sequence, since the position of a term must always be a natural number.