Question

Consider an arithmetic sequence whose 6th term is 40 and 9th term is 58
a-find the common difference?
b-find the 25th term of the sequence?
C-find the sum of first 25th term of the sequence? ​

Answer 1

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Answer 2

Answer:

(i)

6th term is 40.

a + 5d = 40

(ii)

9th term is 58.

a + 8d = 58

On solving (i) & (ii), we get

a + 5d = 40

a + 8d = 58

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

     3d = 18

         d = 6

Substitute d = 6 in (i), we get

a + 5d = 40

a + 30 = 40

a = 10

25th term of the sequence:

aₙ = a + (n - 1) * d

a₂₅ = 10 + (25 - 1) * 6

    = 10 + 24 * 6

    = 154

Sum of first n terms of the sequence:

S₂₅ = (25/2)[2a + (n - 1) * d]

    = (25/2)[20 + (24 * 6)]

    = (25/2)[164]

   =  2050

Step-by-step explanation: