The fifth term of an arithmetic series is 9, and the sum of the first 16 terms is 480. How do you find the first three terms of the sequence?
1 Answer
Solve to find the first term and common difference of the sequence and hence the first three terms:
15/7 ,27/7 ,39/7
Explanation:
The general term of an arithmetic sequence is given by the formula:
a_n = a + d(n-1)
where
The sum of
sum_(n=1)^16 a_n = 16 (a_1 + a_16)/2 = 8(a+(a+15d)) = 16a+120d
From the conditions of the question we have:
240 = 16a + 120d
9 = a_5 = a+4d
Hence:
96 = 240 - 16*9 = (16a+120d) - 16(a+4d)
= color(red)(cancel(color(black)(16a)))+120d - color(red)(cancel(color(black)(16a)))-64d = 56d
So
and
Hence the first three terms of the series are:
15/7 ,27/7 ,39/7