Question 870008
The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is-165.find the 18th term of the sequence

S10=-60
S15=-165

S18=?

Sn = {{{(n/2)(2a+(n-1)d)}}}

S10-{{{(10/2)(2a+9d)}}}

-60= 10a+45d..............(1)

S15 = (15/2)(2a+14d)
-165=(15/2)(2a+14d)
-330 =30a+210d.............(2)

d=	common difference							
a=	first term							
 								
45	d	+	10	a	=	-60	.............1	
Total value								
210	d	+	30	a	=	-330	.............2	
Eliminate	y							
multiply (1)by		-3						
Multiply (2) by		1						
-135	d		-30	a	=	180		
210	d	+	30	a	=	-330		
Add the two equations								
75	d				=	-150		
/	75							
d	=	-2.00						
plug value of			d	in (1)				
45	d	+	10	a	=	-60		
-90		+	10	a	=	-60		
			10	a	=	-60	+	90
			10	a	=	30		
				a	=	3		
d=	-2		common difference					
a=	3		first term					
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