Find the sum of a 28–term arithmetic sequence where the first term is 12 and the last term is 255

Kareem Mejia

Kareem Mejia

Answered question

2022-11-18

Find the sum of a 28–term arithmetic sequence where the first term is 12 and the last term is 255

Answer & Explanation

Pignatpmv

Pignatpmv

Beginner2022-11-19Added 22 answers

To calculate the 'sum to n terms' of an arithmetic sequence use:
S n = n 2 [ 2 a + ( n - 1 ) d ]
the common difference d , is required.
28th term = a + (n-1)d = 12 +27d =255 , hence 27d = 243
hence d = 9.
S 28 = 28 2 [ ( 2 × 12 ) + ( 27 × 9 ) ]
= 14 ( 24 + 243 ) = 14 × 267 = 3738

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