what is the n^th term
what is a's answer
n^th term is:
n (position in sequence) 1 2 3 4 10
value of term 17 20 23 26 a
To find the nth term in this sequence, we can see that the pattern is increasing by 3 each time. So, the nth term can be found by adding 3*(n-1) to the first term.
For example, the 1st term is 17. So, the formula for the nth term is:
nth term = 17 + 3*(n-1)
Now, to find "a's answer", we need to find the value of the 10th term in the sequence.
Using the formula above:
10th term = 17 + 3*(10-1)
= 17 + 3*(9)
= 17 + 27
= 44
Therefore, "a's answer" is 44.
To find the pattern in the given sequence and determine the formula for the n-th term, we can observe the differences between consecutive terms:
1st difference: 20 - 17 = 3
2nd difference: 23 - 20 = 3
3rd difference: 26 - 23 = 3
We can see that the differences between terms are constant at 3. This suggests that the given sequence follows an arithmetic progression with a common difference of 3.
To find the n-th term, we can use the formula for the n-th term of an arithmetic sequence:
a(n) = a(1) + (n - 1)d
where a(n) is the n-th term, a(1) is the first term, n is the position in the sequence, and d is the common difference.
From the given information, we know that the value of the 1st term (a(1)) is 17, and the common difference (d) is 3.
Plugging these values into the formula, we get:
a(n) = 17 + (n - 1)3
Simplifying further:
a(n) = 17 + 3n - 3
Combining like terms:
a(n) = 3n + 14
So, the formula for the n-th term is a(n) = 3n + 14.