in a sequence the 50th term is 349 51st term is 354 and the 52nd term is 359 what is the first and the 100th term
It seems like each term differs by 5.
For the first term, 349 - 49(5) = ?
Use a similar process for the 100th term.
456
To find the first and 100th term of the sequence, we need to determine the pattern governing the sequence. In this case, it seems that each term is increasing by 5.
Let's verify this pattern by finding the difference between consecutive terms in the sequence:
Difference between 50th and 51st term = 354 - 349 = 5
Difference between 51st and 52nd term = 359 - 354 = 5
As the difference between consecutive terms is consistently 5, we can conclude that the sequence is an arithmetic sequence with a common difference of 5.
Now we can find the first term and 100th term of the sequence.
To find the first term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1) * d
Where:
an is the nth term,
a1 is the first term,
n is the position of the term,
d is the common difference.
We are given that the 50th term is 349. Let's substitute the values into the formula:
349 = a1 + (50 - 1) * 5
Simplifying the equation:
349 = a1 + 245
Subtracting 245 from both sides:
a1 = 349 - 245
a1 = 104
Therefore, the first term of the sequence is 104.
To find the 100th term, we can use the same formula:
an = a1 + (n - 1) * d
Substituting the values:
an = 104 + (100 - 1) * 5
an = 104 + 99 * 5
an = 104 + 495
an = 599
Therefore, the 100th term of the sequence is 599.
In summary, the first term of the sequence is 104 and the 100th term is 599.