Given an arithmetic progression with a20 =70 and s20=640 find the first term and the common difference ?

1 Answer
Jim G.
Feb 20, 2018

#a_1=-6" and "d=4#

Explanation:

#"using the "color(blue)"arithmetic sequence formulae"#
#"for the n th term and sum to n terms"#

#•color(white)(x)a_n=a+(n-1)d#

#•color(white)(x)S_n=n/2[2a+(n-1)d]#

#a_(20)=70rArra+19d=70to(1)#

#S_(20)=640rArr10(2a+19d)=640#

#"which simplifies to "2a+19d=64to(2)#

#(1)xx2to2a+38d=140to(3)#

#(3)-(2)to19d=76rArrd=4#

#"substitute "d=4" in equation "(1)#

#a+76=70rArra=70-76=-6#

#"first term "=-6" and common difference "=4#

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