Question

The third term of an A.P is 9 and the difference of the seventh and the second term is 20. If the number 2001 is the nth term of the sequence then n is
(A)equal to 499
(B)is equal to 500
(C)equal to 501
(D)can have no value​

Answer 1

Step-by-step explanation:

According to question

Since it is an AP

first term = a

difference = d

nth term = a n

Thus According to question

third term

a (3 ) = a + (n-1) d

      8  = a + (3-1)d

a + 2d = 8           Eqn 1

Similarly

9th term

a (9) = a + 8d      Eqn 2

And According to question

a(9) = 3 a (3) + 2

a + 8d = 3 * 8 + 2

a+ 8d = 26            Ean 3

Thus a = 26 - 8d

Putting a in Eqn 1

26 - 8d + 2d = 8

26 - 8 = 6 d

d= 3

Thus

a = 26 - 24 = 2

Thus

S (19) = 19/2 [ 2*2 + (19-1)3 ]

           = 551

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