The third term of an arithmetic sequence is 43 and sixth term is 76. what is the common difference?.Find out the first term? .What is the 26th term?
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★ General terms of an A.P.
⇒ Tₙ = a + (n - 1)d.
⇒ T₃ = 34.
⇒ T₃ = a + (3 - 1)d.
⇒ T₃ = a + 2d.
⇒ a + 2d = 34. ⇒ (1).
⇒ T₆ = 67.
⇒ T₆ = a + (6 - 1)d.
⇒ T₆ = a + 5d.
⇒ a + 5d = 67. ⇒ (2).
From equation (1) & (2), we get.
⇒ a + 2d = 34.
⇒ a + 5d = 67.
We get,
⇒ - 3d = - 33.
⇒ d = 11.
Put the value of d = 11 in equation (1), we get.
⇒ a + 2d = 34.
⇒ a + 2(11) = 34.
⇒ a = 34 - 22.
⇒ a = 12.
First term = a = 12.
Common difference = d = 11
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