Find the first term of an a.p. if the sum of the first 10 terms is 150 and d =3.

Le a1, a2, ...,
a10 are terms of an A.P

given S10 = a1+a2+...+10 = 150

But
we know that:

s10 = (a1+a10)*10/2 = 150

==> a1+a10 =
150/5

==> a1+a10 = 30

==> a10 = 30 -
a1......(1)

But a10 = a1 + 9*3 = a1 + 27

==> a10 = 27 +
a1........(2)

from (1) and (2):

==> 30 - a1 = 27 +
a1

==> 2a1 = 3

==> a1= 3/2