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## Answers

d=3

an=X

an=a+(n-1)d

x=1+3n-3

=3n-2

Sn=287

Sn=n/2 (a+an)

=n/2 (1+3n-2)

287 =n/2 (3n-1)

574=3n^2-n

3n^2-n-574=0

now by finding the value of n by quadratic formula . Then substitute the value of n in an

287 = n/2 (2*1 +(n-1) 3)

287*2 = n(2 + 3n - 3)

574 = 2n + 3n^2 - 3n

3n^2 -n - 574 = 0

on solving the quadratic equation using formula n= -b

__+__sq.root(b^2 -4ac)

-----------------------

2a

we get n = 14, -41/3 n not equal to -41/3 due to negative nos.

n=14

Sn = n/2 (a +l)

287 = 14/2(1 +x)

574 = 14 (1+x)

574 / 14 = 1+x

41 = 1 + x

So, x = 41 - 1

x = 40 is the solution