Find the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13

Zack Chase

Zack Chase

Answered question

2022-09-25

Find the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13

Answer & Explanation

Jamari Morgan

Jamari Morgan

Beginner2022-09-26Added 10 answers

In an arithmetic sequence, whose first term is a and difference between a term and its preceding term is d,
the n t h term is a+(n−1)d and sum of first n terms is n 2 ( 2 a + ( n - 1 ) d )
Hence 6 t h term will be a+5d=8 and 10 t h term will be a+9d=13
Subtracting first from second, 4d=5 or d=1.25
and a = 8 - 5 1.25 = 8 - 6.25 = 1.75
Hence sum of first four terms is
4 2 ( 2 1.75 + 3 1.25 ) = 2 ( 3.5 + 3.75 ) = 2 7.25 = 14.50

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