Find the value of n given First term is a=-16, Common difference d=8, the sum of first n terms is 600?

joguejaseg 2022-09-21 Answered
Find the value of n given First term is a=-16, Common difference d=8, the sum of first n terms is 600?
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Answers (1)

Jacey Humphrey
Answered 2022-09-22 Author has 7 answers
This is an Arithmetic sequence
The sum of the first n terms of this sequence is given by.
S n = n 2 [ 2 a + ( n - 1 ) d ]
where a is the first term and d , the common difference.
here a = -16 , d = 8 and require to solve for n.
hence : n 2 [ ( 2 × - 16 ) + 8 ( n - 1 ) ] = 600
n 2 [ - 32 + 8 n - 8 ] = 600 n 2 ( 8 n - 40 ) = 600
distributing gives : 4 n 2 - 20 n - 600 = 0
Equated to zero since this is a quadratic equation.
4 ( n 2 - 5 n - 150 ) = 0
4 ( n + 10 ) ( n - 15 ) = 0 n = - 10 or n = 15
but n > 0 hence n = 15
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