Consider the sequence 1, 4, 7, 10, 13, ....... Can you predict the next four terms? Can you derive the first Class 9

Consider the sequence 1, 4, 7, 10, 13, ....... Can you predict the next four terms? Can you derive the first Class 9

Question 1.

Consider the sequence 1, 4, 7, 10, 13, ....... Can you predict the next four terms? Can you derive the first 10 terms of the sequence obtained by adding all the terms up to a given term of this sequence? Class 9

Answer:

Given sequence: 1, 4, 7,10, 13 ....

The pattern shows that each term is three more than the previous term

∴ Next 4 terms will be

13 + 3 = 16

16 + 3 = 19

19 + 3 = 22

22 + 3 = 25

First 10 terms of sequence obtained by adding all terms to upto a given term is given by:

1st term (t₁): 1

2nd term (t₂): 1+4 = 5

3rd term (t₃): 1 + 4 + 7 = 12

4th term (t₄): 1 + 4 + 7 +10 = 22

5th term (t₅): 1 + 4 + 7 + 10 + 13 = 35

6th term (t₆): 35 + 16 = 51

7th term (t₇): 51 + 19 = 70

8th term (t₈): 70 + 22 = 92

9th term (t₉): 92 + 25 = 117

10th term (t_10): 117 + 28 = 145