Question

If nth term of an A.P is 7+3n, then 20th term of A.P is

Answer 1

Answer:

67

Step-by-step explanation:

Formula for nth term

• an = a + (n-1)d

Given formula brought to same format

• an = 7 + 3n = 10 + 3(n-1)

20th term

• a20 = 10 + 3*19 = 10 + 57 = 67

Answer 2

Answer:

You are in 10th class, am I right...

short answer =

nth term = 7-3n

n=1 = 7-3[1]=4,

n=2 = 7 -3[2] =1,

n=3 =7-3[3]=7-9=-2 ... and so on

so the common difference is 3

20th term = 7-3[20]=-53

Step-by-step explanation:

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