Question

If the 21 th term of an A. P.is 25. Find the sum of its first 41 terms

Answer 1

Given:- a21=25

since, an=a+(n-1)d

=) a21=a+20d ------1)
since , a21=25 (given)

=) a+20d=25
=)a=25-20d -------2)

Since, sum of 'x' terms of an A.P=) Sn=n/2[2a+(n-1)d]
=)41st term (s41) =) 41/2(2(25 - 20d) + (41 - 40) × d

                       = 41/2(2(25 - 20d) + 40d)

                       = 41/2(50 - 40d + 40d)

                       = 41/2(50)

                       = 41 × 25

                        = 1025.


Therefore, the sum( Sn) = 1025..

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