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



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