Question 29 of 51intermediate🔧 ApplyShort Answer5 marks

Check whether the following sequences are geometric progressions and find their nthn^{th} terms. (i) 2, 10, 50, 250, … (ii) 4, 83\frac{8}{3}, 169\frac{16}{9}, 3227\frac{32}{27}, … (iii) 3, −32\frac{-3}{2}, 34\frac{3}{4}, −38\frac{-3}{8}, …

(i)
Answer

Yes, it is a GP. The nth term is 2×52 \times 5^(n-1)

(ii)
Answer

Yes, it is a GP. The nth term is 4 × (2/3)^(n-1)

(iii)
Answer

Yes, it is a GP. The nth term is 3 × (-1/2)^(n-1)

Explanation

A sequence is a geometric progression (GP) if the ratio of consecutive terms is a constant, known as the common ratio. The nth term of a GP is calculated using the formula t_n = ar^(n-1), where 'a' is the first term and 'r' is the common ratio. By evaluating the ratios of consecutive pairs of terms for each sequence, we can verify if they are GPs and subsequently find their nth terms.

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