The 12th term of an AP is -41, given that first term is 3. Find the 20th term
so ... 11 differences (1st to 12th terms) equals ... -41 - 3 = -44
the difference between consecutive terms is ... -44 / 11 = -4
the 20th term is 19 differences from the 1st term ... t20 = 3 + (19 * -4)
To find the 20th term of an arithmetic progression (AP), we need to know the first term and the common difference of the AP.
Given that the first term (a₁) is 3 and the 12th term (a₁₂) is -41, we can find the common difference (d) using the formula:
a₁₂ = a₁ + (n - 1) * d
where n is the term number.
Let's substitute the given values:
-41 = 3 + (12 - 1) * d
Simplifying,
-41 = 3 + 11d
Subtracting 3 from both sides,
-44 = 11d
Dividing both sides by 11,
d = -4
Now that we know the common difference, we can find the 20th term (a₂₀):
a₂₀ = a₁ + (n - 1) * d
Substituting the known values,
a₂₀ = 3 + (20 - 1) * (-4)
Simplifying,
a₂₀ = 3 + 19 * (-4)
a₂₀ = 3 + (-76)
a₂₀ = -73
Therefore, the 20th term of the arithmetic progression is -73.
To find the 20th term of an arithmetic progression (AP) given the 12th term and the first term, we need to determine the common difference.
In an AP, the nth term can be calculated using the formula:
An = A1 + (n - 1)d
Where:
An = nth term of the AP
A1 = first term of the AP
n = position of the term in the AP
d = common difference between consecutive terms
We are given that the first term (A1) is 3 and the 12th term (A12) is -41. We can substitute these values into the formula to find the common difference (d):
-41 = 3 + (12 - 1)d
Simplifying the equation:
-41 = 3 + 11d
Rearranging the equation to isolate the common difference:
11d = -41 - 3
11d = -44
d = -44 / 11
d = -4
The common difference (d) is -4. Now we can use this common difference in the formula to find the 20th term (A20):
A20 = A1 + (20 - 1)d
Substituting the values:
A20 = 3 + (20 - 1)(-4)
Simplifying the equation:
A20 = 3 + 19(-4)
A20 = 3 - 76
A20 = -73
Therefore, the 20th term of the arithmetic progression is -73.