a. An arithmetic sequence has a 10th term 17 and 14th term of 30.
what is the common difference?
Yygfyyuiio
To find the common difference of an arithmetic sequence, we can use the formula:
n-th term = first term + (n - 1) * common difference
Given that the 10th term is 17, we can substitute this into the formula:
17 = first term + (10 - 1) * common difference
Simplifying the equation:
17 = first term + 9 * common difference ...(1)
Similarly, given that the 14th term is 30, we can substitute this into the formula:
30 = first term + (14 - 1) * common difference
Simplifying the equation:
30 = first term + 13 * common difference ...(2)
Now, we can solve these two equations simultaneously to find the common difference:
Subtract equation (1) from equation (2):
30 - 17 = first term + 13 * common difference - (first term + 9 * common difference)
13 = 13 * common difference - 9 * common difference
13 = 4 * common difference
Divide both sides by 4:
common difference = 13/4
Therefore, the common difference of the arithmetic sequence is 13/4 or 3.25.
To find the common difference of an arithmetic sequence, you need to use 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 of the sequence
a1 is the first term of the sequence
n is the position of the term in the sequence
d is the common difference
In this case, we are given that the 10th term of the sequence is 17 and the 14th term is 30. So, we can write two equations using the formula above:
a10 = a1 + (10 - 1)d
17 = a1 + 9d ------(Equation 1)
a14 = a1 + (14 - 1)d
30 = a1 + 13d ------(Equation 2)
Now we can solve this system of equations to find the values of a1 and d. Subtract Equation 1 from Equation 2:
30 - 17 = (a1 + 13d) - (a1 + 9d)
13 = 4d
Divide both sides by 4:
d = 13/4
Therefore, the common difference in the arithmetic sequence is 13/4 or 3.25.