Example 4 - Chapter 5 Class 10 Arithmetic Progressions

Transcript

Example 4 Which term of the AP : 21, 18, 15, . . . is – 81? Also, is any term 0? Give reason for your answer. 21, 18, 15, …………. We need to find, which term is – 81. an = a + (n – 1)d Here an = – 81 , a = 21 & d = 18 – 21 = – 3 We find to find n Putting these in formula an = a + (n – 1) d – 81 = 21 + (n – 1) ( – 3) – 81 = 21 + n ( – 3) – 1( – 3) – 81 = 21 – 3n + 3 – 81 = 24 – 3n 3n = 24 + 81 3n = 105 n = 105/3 n = 35 Therefore the 35th term of given AP is – 81, Now we have to find which term is 0. an = a + (n – 1)d Here an = 0 , a = 21 & d = – 3 We find to find n Putting these in formula an = a + (n – 1) d 0 = 21 + (n – 1) ( – 3) 0 = 21 + n ( – 3) – 1( – 3) 0 = 21 – 3n + 3 0 = 24 – 3n 3n = 24 n = 24/3 n = 8 Therefore the 8th term of given AP is 0,