Question

In each sequence, find:- ¡) general rule ¡¡)nth term ¡¡¡)100th term a) 34,29,24,.....​

Answer 1

Given: the sequence 34, 29, 24, ...

To find:

• i) general rule
• ii) nth term
• iii) 100th term

Solution:

• The first term of the given sequence is 34 and since the common difference is (29 - 34) = (24 - 29) = - 5, it is an Arithmetic Sequence.

• i) General rule: we know aₙ = a₁ + (n - 1) d; substitute 34 for a₁ and (- 5) for d and put any natural n to find the desired term.

• ii) Thus nth term = 34 + (n - 1) (- 4)
• = 34 - 4n + 4
• = 38 - 4n

• iii) So 100th term = 38 - 4 × 100
• = 38 - 400
• = - 362