Find the sum of the first 157 terms of an AP whose first term and third term are 160 and 170 respectively.

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UP Police SI (दरोगा) Official PYP (Held On: 12 Nov 2021 Shift 3)
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  1. 86350
  2. 83350
  3. 84350
  4. 85350

Answer (Detailed Solution Below)

Option 1 : 86350
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यूपी पुलिस SI (दरोगा) सामान्य हिंदी मॉक टेस्ट
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Detailed Solution

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Given:

First term (a) = 160

Third term = 170

Total terms (n) = 157

Formula Used:

Sum of first n terms of an AP (Sn) = n/2 × [2a + (n - 1) × d]

Common difference (d) = (Third term - First term) / (3 - 1)

Calculation:

d = (170 - 160) / 2

⇒ d = 10 / 2

⇒ d = 5

S157 = 157/2 × [2 × 160 + (157 - 1) × 5]

⇒ S157 = 157/2 × [320 + 156 × 5]

⇒ S157 = 157/2 × [320 + 780]

⇒ S157 = 157/2 × 1100

⇒ S157 = 157 × 550

⇒ S157 = 86350

The sum of the first 157 terms is 86350.

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