# 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?

##### 1 Answer

Feb 27, 2016

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