The third and seventh terms of an arithmetic sequence are 10 and 20.
1) What is the value of the 1st term?
2) What is the value of the 9th term?
3) What is the equation to find the nth term in the sequence?
HELP!! PLEASE!!
Arithmetic sequence
a, a + d, a + 2d, a + 3d, ...a +(n - 1)d
1)a3 = 10, a7 = 20
Since these are 4 places apart (7 - 3 = 4)
a7 = a3 + 4d
20 = 10 + 4d
10 = 4d
d = 10/4 = 2.5
So, the common difference, d = 2.5
To find the 1st term a,
a3 = a + 2d
10 = a + 2(2.5)
10 = a + 5
a = 5
2) to find 9th term
a9 = a + 8d
a9 = 5 + 8(2.5)
a9 = 5 + 20
a9 = 25
3) nth term
Last term = a + (n - 1)d
an = 5 + (n - 1)(2.5)
4a2
To find the value of the 1st term, we need to find the common difference (d) first. The common difference helps us determine how each term in the sequence is related to the previous term.
To find the common difference, we can subtract the third term from the seventh term: 20 - 10 = 10.
Knowing the common difference is 10, we can now find the first term by subtracting 2 times the common difference from the third term: 10 - 2 * 10 = -10.
So, the value of the 1st term is -10.
To find the value of the 9th 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 is the first term, n is the position of the term in the sequence, and d is the common difference.
Plugging in the known values, we have:
A9 = (-10) + (9 - 1) * 10 = -10 + 8 * 10 = -10 + 80 = 70.
So, the value of the 9th term is 70.
The equation to find the nth term in the sequence, as mentioned earlier, is:
An = A1 + (n - 1) * d.
Where An represents the nth term, A1 is the first term, n is the position of the term in the sequence, and d is the common difference.