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in Arithmetic Progression by (31.2k points)
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Find the sum of first 51 terms of AP. in which IInd and IIIrd term are 14 and 18 respectively.

1 Answer

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Best answer

Second term of A.P. a2 = 14

and third term a3 = 18

∴ Common difference d = a3 – a2

= 18 – 14 = 4

Again, ∵ IInd term = 14

∴ a + d = 14

⇒ a + 4 = 14

⇒ a = 14 – 4

⇒ a = 10

∵ a = 10, d = 4

Then, sum of n terms 

Sn = n/2[2a + (n – 1)d]

∴ S51 = 51/2[2 × 10 + (51 – 1)4]

= 51/2[20 + 50 × 4]

= 51/2[20 + 200]

= 51/2 × 220 = 51 × 110 = 5610

Hence, sum of 5 terms of given A.P. = 5610

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