Chapter 8
Predicting What Comes Next: Exploring Sequences and Progressions
CBSE Class 9
Mathematics Solutions
Educart Mathematics class Class 9 NCERT Exemplar cover
Question:

A sequence is given by the recursive rule t1=2t_1 = 2, tn+1=3tn−2t_{n+1} = 3t_n - 2 for n≥1n \geq 1. Which term of the sequence is 730?                                                                                                                                                                                                     [Page No. 193]

Answer: Verified

Given tn+1=3tn−2\text{Given }t_{n+1}=3t_{n}-2

Terms: t1=2\text{Terms: } t_1 = 2

t2=3(2)−2=4t_2 = 3(2) - 2 = 4

t3=3(4)−2=10t_3 = 3(4) - 2 = 10

t4=3(10)−2=28t_4 = 3(10) - 2 = 28

t5=3(28)−2=82t_5 = 3(28) - 2 = 82

t6=3(82)−2=244t_6 = 3(82) - 2 = 244

t7=3(244)−2=730t_7 = 3(244) - 2 = 730

Therefore, 7th term of the sequence is 730.

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More NCERT Questions
Can the same approach (refer to NCERT page no. 183) be used to find the sum of 1 + 2 + 3 + + 100? [Page No. 184] Observe the Sierpiński triangle. (A) How many black triangles are there in Stages 0 to 3? (B) Predict the number at Stages 4 and 5. (C) Find a rule for the number of black triangles at the nth stage. Can you use this formula to find S20, S50 or S1000? [Page No. 185] Let us revisit the sequence tn of triangular numbers 1, 3, 6, 10, 15, shown in the given figure. Note that the nth term of this sequence is the sum of the first n natural numbers. Thus, tn = n(n + 1)/