Find the sum of the arithmetic series 2 + 5 + 8 + ... + 56

excefebraxp 2022-09-14 Answered
Find the sum of the arithmetic series 2 + 5 + 8 + ... + 56
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Answers (1)

Grace Moses
Answered 2022-09-15 Author has 13 answers
The first term of the corresponding arithmetic sequence is a=2 and the common difference between successive terms is d=3.
Hence the general term may be given by the formula
( x n ) = a + ( n - 1 ) d
= 2 + ( n - 1 ) ( 3 )
= 3 n - 1
So we now need to find which term has value 56 so that we know how many terms to sum up to.
56 = 3 n - 1 n = 57 3 = 19
So we thus need to find the sum of the series n = 1 19 ( 3 n - 1 )
There are 2 formulae applicable :
1. S n = n 2 [ 2 a + ( n - 1 ) d ]
= 19 2 [ 2 ( 2 ) + ( 19 - 1 ) ( 3 ) ]
= 551
2. S n = n 2 ( a + l )
= 19 2 ( 2 + 56 )
= 551

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