Question

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!!

Answer 1

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)

Answer 2

4a2