Why is it useful to have an explicit formula for the nth term of a sequence? Class 9

Why is it useful to have an explicit formula for the n^th term of a sequence? Class 9

Question 1.

Why is it useful to have an explicit formula for the n^th term of a sequence ? Class 9

Answer:

It helps to find any term directly without writing all previous terms. We can easily find large terms like the 50^th or 100^th term of a sequence.

Question 2.

Using the explicit rule u_n = 2n - 1. Find 53^rd term, the 108^th term and the 1170^th term of odd number sequence. Class 9

Answer:

Explicit rule for odd numbers sequence is given by.

u_n = 2n - 1 ...(i)

Putting n = 53 in (i), we get

∴ u₅₃ = 2 (53) - 1

= 105

Putting n = 108 in (i), we get

∴ u₁₀₈ = 2(108) - 1

= 215

Putting n = 1170 in (i), we get

∴ u₁₁₇₀ = 2(1170) - 1

= 2339