Find a_1a1 if the given are S_n=195, a_n=33 and d=3 ?Sn=195,an=33andd=3?

Arithmethic Sequence

1 Answer
Jul 19, 2018

a_1=-3, or, 6a1=3,or,6.

Explanation:

In the Usual Notation of an AP,

S_n=n/2{a_1+a_n}Sn=n2{a1+an}.

:. 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.