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