The first and the last terms of an Arithmetic Progression are 6 and 171 in that order. If there are 14 terms, find the 16th term of the Arithmetic Progression.
given:
a = 6
a + 13d = 171
6+13d = 171
13d = 165
d = 165/13
term16 = term14 + 2d
= 171 + 330/16 = 2553/13
term 16 = a + 15d
= 6 + 15(165/13) = 2553/13
Not correct
Why did the arithmetic progression become a comedian? Because it couldn't resist telling a "series" of hilarious jokes along the way! Now, let's calculate the 16th term.
In an Arithmetic Progression, we know that the difference between consecutive terms is always the same. We can calculate this difference using the first and the last terms.
The common difference (d) can be found using the formula d = (last term - first term) / (number of terms - 1). Let's plug in the values:
d = (171 - 6) / (14 - 1) = 165 / 13 = 15
Now that we know the common difference, we can find the 16th term using the formula: nth term = first term + (n - 1) * d
16th term = 6 + (16 - 1) * 15 = 6 + 15 * 15 = 6 + 225 = 231
So, the 16th term of the Arithmetic Progression is 231. Don't worry, no arithmetic progressions were harmed during the calculation!
To find the 16th term of the Arithmetic Progression, we first need to determine the common difference (d) of the sequence.
We know that the first term (a₁) is 6 and the last term (aₙ) is 171. We also know that the number of terms (n) is 14.
The formula to find the nth term (aₙ) of an arithmetic sequence is:
aₙ = a₁ + (n - 1) * d
We can plug in the given values:
171 = 6 + (14 - 1) * d
Simplifying the equation:
171 = 6 + 13d
Subtracting 6 from both sides:
165 = 13d
Dividing both sides by 13:
d = 165 / 13
d = 12.6923 (approx.)
Now that we have the common difference (d), we can find the 16th term (a₁₆) using the formula mentioned earlier:
a₁₆ = a₁ + (16 - 1) * d
Plugging in the values:
a₁₆ = 6 + 15 * 12.6923
Calculating:
a₁₆ ≈ 6 + 190.3846
a₁₆ ≈ 196.3846
Therefore, the 16th term of the Arithmetic Progression is approximately 196.3846.