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State True/False.

The sum of the AP 3,5,7,9,11…….. ‘s 6th and 13th term is 40, and its 4th term is 9.

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True

False

answer is A.

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Detailed Solution

Given that the 4th term of A.P. is 9 and the sum of its 6th and 13th terms is 40.
Let a be the first term and d be the common difference of the AP.
Applying formula:

a n = a + n − 1 d

a 4 = 9

⇒ a + (4 − 1) d = 9 ⇒ a + 3 d = 9 … … … ...... (1)

a 6 + a 13 = 40 ⇒ (a + 5 d) + (a + 12 d) = 40 ⇒ 2 a + 17 d = 40 … … … ...... (2)

From equation (1) & (2), we have,

⇒ 2 (9 − 3 d) + 17 d = 40 ⇒ 18 − 6 d + 17 d = 40 ⇒ 11 d = 40 − 18 ⇒ 11 d = 22

Thus, d = 2
Put the value of d in equation (1)

⇒ a + 3 × 2 = 9 ⇒ a = 9 − 6 = 3

Therefore, the AP is 3,5,7,9,11........
Thus, the given statement is true.
Hence, option (1) is correct.

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