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So if we call the first term of the sequence A,and the common difference d, then the formula for the nth term is A+ [(n-1)d] this just comes from understanding that the first term is A the second term is A+d the third is A+2d the 4th is A+ 3d so the nth term is A + (n-1)d. So let's set up two equations and solve them for A and d and then we are done A+ 8d=90 A+15d=153 This is the same as -A-8d=-90 A+15d=153 and we add these two equation to eliminate A. This is called elimination. You can also solve this system of 2 equations in 2 unknowns with substitution by substituting A=90-8d into the second equation. I think this is harder We have 7d=63 so d=9 and then plug that into either equation and A=18 So the first 4 terms are 18, 18+9, 18+18, 18+27 or we write 18, 27, 36, 45

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Q: What are the first 4 terms of an arithmetic sequence if the ninth term is 90 and the sixteenth term is 153?
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