Ex 8.3, 1 - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

Transcript

Ex 8.3, 1 Find the 12th term of a GP with common ratio 2 , whose 8th term is 192. We know that for a GP nth term = 𝒂_𝒏=〖𝒂𝒓〗^(𝒏−𝟏) Given that Common ratio = r = 2 Also, given that 8th term is 192 8th term = 192 a8 = 192 Putting n = 8, r = 2 in an formula 𝒂 × 𝟐^(𝟖 − 𝟏)=𝟏𝟗𝟐 𝑎 × 2^7=192 𝒂=𝟏𝟗𝟐/𝟐^𝟕 Now, we need to find 12th term, Using our formula 𝒂_𝒏=〖𝒂𝒓〗^(𝒏−𝟏) Putting n = 12 , a = 192/27 , r = 2 𝒂_𝟏𝟐=𝟏𝟗𝟐/𝟐𝟕 × 𝟐^(𝟏𝟐 − 𝟏) 𝑎_12=192/27 × 2^11 𝑎_12=192 ×2^11/2^7 𝑎_12=192 × 2^(11 − 7) 𝒂_𝟏𝟐=𝟏𝟗𝟐 × 𝟐^𝟒 𝑎_12=192 × 16 𝒂_𝟏𝟐=𝟑,𝟎𝟕𝟐 Thus, 12th term is 3072