Ex 8.1, 5

Transcript

Ex 8.1, 5 A sequence is given by the recursive rule 𝑡_1=−5,𝑡_(𝑛+1)=𝑡_𝑛+3 for 𝑛≥1. Find the first five terms of the sequence. Is 52 a term of this sequence? If so, which term is it? First, let’s find first five terms i.e. 𝒕_𝟏, 𝒕_𝟐, 𝒕_𝟑, 𝒕_𝟒, 𝒕_𝟓 Given First term = 𝒕_𝟏 = –5 Second term = 𝑡_2 = 𝑡_(1 + 1) = 𝒕_𝟏+𝟑 = –5 + 3 = –2 Third term = 𝑡_3 = 𝑡_(2 + 1) = 𝒕_𝟐+𝟑 = –2 + 3 = 1 Fourth term = 𝑡_4 = 𝑡_(3 + 1) = 𝒕_𝟑+𝟑 = 1 + 3 = 4 Fifth term = 𝑡_5 = 𝑡_(4 + 1) = 𝒕_𝟒+𝟑 = 4 + 3 = 7 The first five terms are –5, –2, 1, 4, 7 Now, we are asked Is 52 a term of this sequence? If so, which term is it? We notice that we are adding 3 to our terms So, our next terms would be 6th term = 7 + 3 = 10 7th term = 10 + 3 = 13 8th term = 13 + 3 = 16 9th term = 16 + 3 = 19 10th term = 19 + 3 = 22 11th term = 22 + 3 = 25 12th term = 25 + 3 = 28 13th term = 28 + 3 = 31 14th term = 31 + 3 = 34 15th term = 34 + 3 = 37 16th term = 37 + 3 = 40 17th term = 40 + 3 = 43 18th term = 43 + 3 = 46 19th term = 46 + 3 = 49 20th term = 49 + 3 = 52 Thus, 52 is the 20th term of the sequence