InterviewSolution
| 1. |
Find the A.P. whose nth term is 7 - 3n. Also find the 20th term. |
|
Answer» Since you gave an explicit formula for the AP, we can just plug in values for n, as shown below: 0 -> 7 1 -> 4 2 -> 1 3 -> -2 … So the AP is; 7, 4, 1, -2, -5, -8, … With a common difference of -3. Before I answer your second part, I have to talk about something first. You might have noticed that the first term of the sequence is n = 0, not 1. I personally like this better for reasons beyond the scope of this answer (but I will say that it’s because of arithmetic series), but it is reasonable to have 0 or 1 as your first term. If you choose to have your first term as n = 1, then the sequence would be the same, but without the 7. 4, 1, -2, -5, -8, -11… So the answer is different depending on how you define your sequence. If the first term is n = 0, then to find the 20th term, set n = 20 - 1 = 19 7 -3(19) = -50 If the first term is n = 1, then to find the 20th term, set n = 20 7 -3(20) = -53 nth term = 7-3nn=1 = 7-3[1]=4,n=2 = 7 -3[2] =1,n=3 =7-3[3]=7-9=-2 ... and so onso the common difference is 320th term = 7-3[20]=-53 |
|