the 12th term of an A.P is -14, given that the first term is 3, find the 20th term
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Well, if the 12th term of an A.P is -14 and the first term is 3, we can find the common difference.
Let's call the common difference "d".
The 12th term can be found using the formula: aₙ = a₁ + (n-1)d, where aₙ is the nth term.
Plugging in the values we know, we get: -14 = 3 + (12-1)d
Simplifying, we have: -14 = 3 + 11d
Subtracting 3 from both sides gives us: -17 = 11d
Finally, dividing both sides by 11, we find: d = -17/11
Now, to find the 20th term, we can use the same formula. Plugging in the values, we get:
a₂₀ = 3 + (20-1)(-17/11)
Calculating, we find:
a₂₀ = 3 + 19*(-17/11) = 3 - 323/11 = -290/11
So, the 20th term of the A.P is approximately -26.36 (rounded to two decimal places).
Remember, math can be funny sometimes too!
To find the 20th term of an arithmetic progression (A.P.), we need to determine the common difference (d) first. The formula for the nth term of an A.P. is:
An = a + (n-1)d
Given that the 12th term (A12) is -14 and the first term (A1) is 3, we can substitute these values into the formula and solve for 'd'.
A12 = 3 + (12-1)d
-14 = 3 + 11d
11d = -14 - 3
11d = -17
Dividing both sides by 11, we get:
d = -17/11
Now that we have the value of 'd', we can find the 20th term (A20) by substituting it back into the formula:
A20 = 3 + (20-1)(-17/11)
A20 = 3 + 19(-17/11)
A20 = 3 - (323/11)
A20 = 3 - 29
A20 = -26
Therefore, the 20th term of the A.P. is -26.
To find the 20th term of an arithmetic progression (A.P.), we need to first determine the common difference of the progression.
The common difference (d) of an A.P. is calculated by subtracting the first term (a₁) from the second term (a₂).
In this given problem, the first term (a₁) is 3, and the 12th term (a₁₂) is -14.
So, we can set up the following equation:
a₁₂ = a₁ + (12 - 1) * d
Substituting the given values:
-14 = 3 + (11) * d
Next, we solve this equation to find the value of 'd' (the common difference):
-14 - 3 = 11d
-17 = 11d
d = -17/11
Now that we know the common difference (d = -17/11), we can find the 20th term (a₂₀) using the formula:
a₂₀ = a₁ + (20 - 1) * d
Substituting the values found:
a₂₀ = 3 + (19) * (-17/11)
a₂₀ = 3 - 17*19/11
a₂₀ = 3 - 323/11
a₂₀ = 3 - 29
a₂₀ = -26
Therefore, the 20th term of the arithmetic progression is -26.