Example 2 - Chapter 5 Class 10 Arithmetic Progressions

Transcript

Example 2 Which of the following list of numbers does form an AP? If they form an AP, write the next two terms : 4, 10, 16, 22 ……………… Difference between 2nd and 1st term = 10 – 4 = 6 Difference between third and second term = 16 – 10 = 6 Difference between fourth and third term = 22 – 16 = 6 Since difference is same, it is an AP Common difference = d = 6 We have to find next two terms We are given 4 terms . So, we have to find 5th and 6th terms . 5th term = 4th term + common difference = 22 + 6 = 28 4, 10, 16, 22,… d = 6Difference between fourth and third term = 22 – 16 = 6 Since difference is same, it is an AP Common difference = d = 6 We have to find next two terms We are given 4 terms . So, we have to find 5th and 6th terms . 5th term = 4th term + common difference = 22 + 6 = 28 4, 10, 16, 22,… d = 6 6th term = 5th term + common difference = 28 + 6 = 34 Hence, 5th and 6th terms are 28 and 34. Example 2 Which of the following list of numbers does form an AP? If they form an AP, write the next two terms : (ii) 1, –1, –3, –5, ………. Difference between 2nd and 1st term = (–1) – (1) = –1 – 1 = –2 Difference between 3rd and 2nd term = –3 – (–1) = –3 + 1 = –2 Difference between 4th and 3rd term = (–5) – (–3) = –5 + 3 = –2 Since difference is same, it is an AP Common difference = d = –2 We have to find next two terms We are given 4 terms . So, we have to find 5th and 6th terms . 5th term = 4th term + common difference = –5 + (–2) = –5 – 2 = –7 6th term = 5th term + common difference = –7 + (–2) = –7 – 2 = –9 Hence the 5th and 6th term of the series are –7 and –9. Example 2 Which of the following list of numbers does form an AP? If they form an AP, write the next two terms : (iii) – 2, 2, –2, 2, –2, …………. Difference between 2nd and 1st term = 2 – ( – 2) = 2 + 2 = 4 Difference between 3rd and 2nd term = –2 – (2) = –2 – 2 = –4 Since, difference is not same . 4 ≠ –4 Hence it is not an AP Example 2 Which of the following list of numbers does form an AP? If they form an AP, write the next two terms : (iv) 1, 1, 1, 2, 2, 2, 3, 3, 3, ………… Difference between 2nd and 1st terms = 1 – 1 = 0 Difference between 3rd and 2nd terms = 1 – 1 = 0 Difference between 4th and 3rd term = 2 – 1 = 1 Since difference is not same 0 ≠1 Hence it is not an AP. Since difference is not same 0 ≠1 Hence it is not an AP.