The fifth term of an arithmetic series is 9, and the sum of the first 16 terms is 480. Find the first three terms of the sequence

fabler107

fabler107

Answered question

2022-11-11

The fifth term of an arithmetic series is 9, and the sum of the first 16 terms is 480. Find the first three terms of the sequence

Answer & Explanation

sliceu4i

sliceu4i

Beginner2022-11-12Added 16 answers

The general term of an arithmetic sequence is given by the formula:
a n = a + d ( n - 1 )
where a is the initial term and d is the common difference.
The sum of N consecutive terms of an arithmetic sequence is N times the average of the first and last terms, so:
n = 1 16 a n = 16 a 1 + a 16 2 = 8 ( a + ( a + 15 d ) ) = 16 a + 120 d
From the conditions of the question we have:
240 = 16 a + 120 d
9 = a 5 = a + 4 d
Hence:
96 = 240 - 16 9 = ( 16 a + 120 d ) - 16 ( a + 4 d )
= 16 a + 120 d - 16 a - 64 d = 56 d
So d = 96 56 = 12 7
and a = 9 - 4 d = 9 - 48 7 = 15 7
Hence the first three terms of the series are:
15 7 , 27 7 , 397 7

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