The 12th term of an A.P is -41.Given that the first term is 3.find the 20th term
What you need is to learn the definitions for an AP, and how to apply it
a = 3
term(12) = a + 11d = -41
3 + 11d = -41
solve for d, and then
term(20) = a + 19d = ....
I need it now please
Well, the 12th term is -41 and the first term is 3. That means we have quite a negative situation going on here! It seems like our A.P. is having a bad day.
But fear not, because using the information we have, we can find a solution that will surely put a smile on your face. Let's calculate the common difference of the A.P.
The formula for the nth term in an A.P. is given by:
an = a + (n-1)d
Here, a represents the first term, n represents the term number, and d represents the common difference.
Plugging in the values we have:
-41 = 3 + (12-1)d
Simplifying, we get:
-41 = 3 + 11d
Distributing on the right side:
-41 = 3 + 11d
Subtracting 3 from both sides:
-44 = 11d
Taking a giant leap forward, dividing both sides by 11, we find:
d = -4
Now that we know the common difference is -4, we can use the formula to find the 20th term:
a20 = a + (20-1)d
Plugging in the known values:
a20 = 3 + (20-1)(-4)
Simplifying, we have:
a20 = 3 + 19(-4)
Doing some math gymnastics, we find:
a20 = 3 - 76
Drumroll, please...
The 20th term of the A.P. is: -73.
So, amidst all the negativity, it seems like our A.P. ended up at -73 for its 20th term. Keep your chin up, A.P., things will get better!
I need it now
To find the 20th term of an arithmetic progression (A.P.), we need to use the formula:
an = a + (n - 1)d
Where:
an is the nth term of the A.P.
a is the first term of the A.P.
n is the position of the term in the A.P.
d is the common difference between the terms of the A.P.
In this case, the first term (a) is 3, and the 12th term (an) is -41.
We can use this information to find the common difference (d). By substituting the values into the formula, we have:
-41 = 3 + (12 - 1)d
-41 = 3 + 11d
Now, we can solve for the common difference (d):
-41 - 3 = 11d
-44 = 11d
d = -44/11
d = -4
With the common difference (d) determined, we can find the 20th term (a20) using the formula again:
a20 = a + (n - 1)d
a20 = 3 + (20 - 1)(-4)
a20 = 3 + 19(-4)
a20 = 3 - 76
a20 = -73
Therefore, the 20th term of the A.P. is -73.