Find nth term of the sequence 5,8,11...is 383.Find n.
Tn = 2 + 3n
So, you want
2 + 3n = 383
Sure, let's find the nth term of the sequence 5, 8, 11... and see if we can find the value of n when the term is 383.
To find the nth term of a sequence, we observe that the difference between consecutive terms is always 3. So, the sequence can be seen as an arithmetic sequence with a common difference of 3.
Applying the formula for the nth term of an arithmetic sequence, which is given by:
an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
Here, a1 = 5 and d = 3.
So, plugging in the values:
an = 5 + (n - 1)3
Now, let's solve for n when an is 383:
383 = 5 + (n - 1)3
378 = (n - 1)3
126 = n - 1
n = 127
Therefore, the position of the term when the value is 383 is n = 127.
To find the nth term of the sequence 5, 8, 11..., we need to determine the common difference between consecutive terms.
Notice that each term is obtained by adding 3 to the previous term. Therefore, the common difference is 3.
We now have the first term (5) and the common difference (3). We can use the formula for the nth term of an arithmetic sequence, which is:
a_n = a_1 + (n - 1)d
where:
a_n is the nth term,
a_1 is the first term,
n is the position of the term we want to find, and
d is the common difference.
In this case, we want to find the value of n when the nth term is 383. So, we can plug in the values we have into the formula:
383 = 5 + (n - 1)3
To solve for n, we can simplify the equation:
383 = 5 + 3n - 3
383 - 5 = 3n - 3
378 = 3n
n = 378/3
n = 126
Therefore, the value of n is 126.
To find the nth term of an arithmetic sequence, we need to determine the common difference first. In this case, the common difference between consecutive terms is 8 - 5 = 3.
We want to find the nth term that equals 383. We can set up an equation using the formula for arithmetic sequences: a + (n - 1)d = T, where a is the first term, d is the common difference, n is the number of terms, and T is the desired term.
Substituting the known values into the equation, we have 5 + (n - 1)3 = 383.
Simplifying the equation, we get 5 + 3n - 3 = 383.
Combining like terms, we have 3n + 2 = 383.
Subtracting 2 from both sides of the equation, we have 3n = 381.
Finally, dividing both sides of the equation by 3, we find n = 127.
Therefore, the 127th term of the sequence is 383.