Find #a_1# if the given are #S_n=195, a_n=33 and d=3 ?#

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Arithmethic Sequence

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Answer 1 · 2018-07-19T09:23:04

# a_1=-3, or, 6#.

In the Usual Notation of an AP,

#S_n=n/2{a_1+a_n}#.

#:. 195=n/2{a_1+33}.........(1)#.

Also, #a_1+(n-1)d=a_n#.

#:. a_1+3(n-1)=33#.

#:. a_1=33-3(n-1)=36-3n#.

Subst.ing in #(1), 195xx2=n{(36-3n)+33},#

# i.e., n(69-3n)=195xx2,#

# or, n(23-n)=(195xx2)/3=65xx2=13xx10#.

#:. n=13, or, 10#.

#:. a_1=36-3n=36-39, or, 36-30#.

#:. a_1=-3, or, 6#.