what is the 10th term in this arithemetic sequence of 2,9,16,23,30?
2,9,16,23,30,37,44,51,58,65
To find the 10th term in an arithmetic sequence, we need to find the common difference first. The common difference is the constant amount that is added to each term to get the next term.
In the given sequence of 2, 9, 16, 23, 30, we can see that each term is obtained by adding 7 to the previous term.
So, the common difference is 7.
To find the 10th term, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
Where:
aₙ represents the nth term
a₁ represents the first term
d represents the common difference
n represents the position of the term we want to find
In this case:
a₁ = 2 (first term)
d = 7 (common difference)
n = 10 (position of the 10th term)
Substituting these values into the formula, we get:
aₙ = 2 + (10 - 1) * 7
= 2 + 9 * 7
= 2 + 63
= 65
Therefore, the 10th term in the sequence 2, 9, 16, 23, 30 is 65.
To find the 10th term in an arithmetic sequence, you'll need to determine the common difference and use the formula for the nth term.
In this sequence, the common difference is 9 - 2 = 7, since each term is obtained by adding 7 to the previous term.
The formula to find the nth term in an arithmetic sequence is:
an = a1 + (n-1)d
where:
an represents the nth term,
a1 is the first term, and
d is the common difference.
In this case, the first term (a1) is 2, and the common difference (d) is 7.
Plugging those values into the formula:
a10 = 2 + (10-1) * 7
= 2 + 9 * 7
= 2 + 63
= 65
Therefore, the 10th term in the given arithmetic sequence is 65.
a=2 , d=7
t(n) = a+(n-1)d
t(10) = a+9d
= .....