Mathematics
Show that the list of numbers 9, 12, 15, 18, … form an A.P. Find its 16th term and the nth term.
Answer
Here,
a2 - a1 = 12 - 9 = 3,
a3 - a2 = 15 - 12 = 3.
i.e. any term - preceding term = 3 = fixed number,
Hence, given list of numbers forms an A.P. with first term = a = 9 and common difference = d = 3.
We know that,
an = a + (n - 1)d = 9 + (n - 1) × 3 = 9 + 3n - 3 = 6 + 3n.
Since, an = 6 + 3n, so
a16 = 6 + 3 × 16 = 6 + 48 = 54.
Hence, the an = 3n + 6 and a16 = 54.