Ex 8.3, 2 - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Ex 8.3, 2 Find the 10th and nth terms of the GP: 5, 25, 125,…. Given GP 5, 25, 125, …. Here, First term = a = 5 Common ratio = r = 25/5 = 5 We know that for a GP nth term = 𝒂_𝒏=〖𝒂𝒓〗^(𝒏−𝟏) Finding nth term Now, 𝒂_𝒏=〖𝒂𝒓〗^(𝒏−𝟏) Putting a = 5, r = 5 =𝟓 × 𝟓^(𝒏−𝟏) =5^1 × 5^(𝑛−1) =5^(1 + 𝑛 − 1) =𝟓^𝒏 Thus, nth term of GP is 𝟓^𝒏 Finding 10th term For 10th term, we put n = 10 in nth term Now, 𝒂_𝒏=〖𝒂𝒓〗^(𝒏−𝟏) Putting a = 5, r = 5 =𝟓 × 𝟓^(𝒏−𝟏) =5^1 × 5^(𝑛−1) =5^(1 + 𝑛 − 1) =𝟓^𝒏 𝑎_𝑛=5^𝑛 Putting n = 10 𝒂_𝟏𝟎=𝟓^𝟏𝟎 Hence, 10th term of GP is 𝟓^𝟏𝟎