Question

The 3rd term of an ap is 8 and the 9th term exceeds 3times the 3rd term by 2 Find the sum of the 19th term ​

Answer 1

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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           (Eqn 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


HOPE IT WILL HELP YOU.......

Answer 2

Answer:

Please refer the attachment dear