Example 9 - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

Transcript

Example 9 Check whether the sequence 5, 15/4, 45/16, 135/64,… is a geometric progression and find its nth term. Given sequence 5, 15/4, 45/16, 135/64,… If its GP, then common ratio is same So, we need to show (𝟐^𝒏𝒅 𝒕𝒆𝒓𝒎)/(𝟏^𝒔𝒕 𝒕𝒆𝒓𝒎)=" " (𝟑^𝒓𝒅 𝒕𝒆𝒓𝒎)/(𝟐^𝒏𝒅 𝒕𝒆𝒓𝒎) Now, (𝟏𝟓/𝟒)/𝟓=(𝟒𝟓/𝟏𝟔)/(𝟏𝟓/𝟒) 15/(4 × 5)=45/(16 ) × 4/15 3/4=3/4 × 1/1 𝟑/𝟒=𝟑/𝟒 Since common ratio is same, it is a GP Now, we need to find nth term Here, First term = a = 5 Common ratio = r = 𝟑/𝟒 Now, nth term = 𝒂_𝒏 = 𝑎𝑟^(𝑛−1) Putting values = 𝟓 × (𝟑/𝟒)^(𝒏−𝟏)