Question

How do you find the value of n given First term is a=-16, Common difference d=8, And the sum of first n terms is 600?

Answer 1

n = 15

Explanation:

This is an`color(blue) " Arithmetic sequence "`

The sum of the first n terms of this sequence is given by.

`S_n = n/2 [ 2a + (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[(2xx-16) + 8(n - 1 ) ] = 600`

`n/2 [ -32 + 8n - 8 ] = 600 rArr n/2( 8n - 40) = 600`

distributing gives : `4n^2 - 20n -600 = 0`

Equated to zero since this is a quadratic equation.

`rArr 4( n^2 - 5n - 150 ) = 0`

`rArr 4(n + 10 )(n -15 ) = 0 rArr n = - 10 or n = 15`

but n > 0 hence n = 15