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In arithmetic progression, the fifth term is 4 less than the ninth term. If the sum of the first 25 terms is 305, then, find the first term of A.P?
1. 1/4
2. 1/5
3. 2/5
4. 1/6

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Correct Answer - Option 2 : 1/5

Given:

The sum of the first 25 terms = 305

Formula used:

Tn = a + (n – 1) d

Sn = n/2 × [2a + (n – 1) d], where a is the first term. n is number of terms and d = common difference.

Calculation:

T5 = a + (5 – 1) d

⇒ T5 = a + 4d     ---- (1)

And T9 = a + 8d      ---- (2)

∴ T9 – T5 = 4

⇒ a + 8d – a – 4d = 4

⇒ 4d = 4

⇒ d = 1

According to question

⇒ 305 = 25/2 × [2a + (25 – 1) 1]

⇒ 122 = 10a + 5(24)

⇒ 122 = 10a + 120

⇒ 10a = 122 – 120

⇒ 10a = 2

⇒ a = 2/10

∴ a = 1/5

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