Lucia knows the fourth term in a sequence is 55 and the ninth term in the same sequence is 90. Explain how she can find the common difference for the sequence. then use the common difference to find the second term of the sequence.

Using the formula for the nth term of an arithmetic progression.

an = a + (n - 1) d

a (4) = a + 3d = 55

a (9) = a + 8d = 90

a (9) - a (4) = > 5d = 35

d = 35/5 = 7.

From a (4) : a = 55 - 3d = 55 - 3 (7) = 55 - 21 = 34

a (2) = a + d = 34 + 7 = 41.