Question

4. In an A.P. the 17th term is 67 and the 34th term is 135, find the sum of the first 50 terms.​
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

a17 = a + 16d = 67

=> a = 67 - 16d ..(1)

a34 = a + 33d = 135

=> a = 135 - 33d

Using equation (1),

=> 67 - 16d = 135 - 33d

=> 33d - 16d = 135 - 67

=> 17d = 68

=> d = 4 .

Using d = 4 in eq. (1), we get

=> a = 67 - (16x4)

=> a = 67 - 64 = 3

Sum of first 50 terms :

[Sn = n/2 ( 2a + (n-1)d ) ]

S50 = 50/2 ( 2(3) + (50-1)4 )

= 25 x ( 6 + 49 x 4 )

= 25 x ( 6 + 196 )

= 25 x 202

= 5050