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If the 3rd and 6th terms of an AP are 7 and 13 .find the first and the common difference. |
Answer» Answer :first term, a = 3 common difference, d = 2 Step-by-step EXPLANATION :nth term of an AP is GIVEN by, aₙ = a + (N - 1)d where a is the first term d is the common difference
a₃ = a + (3 - 1)d 7 = a + 2d -- [1]
a₆ = a + (6 - 1)d 13 = a + 5d -- [2] equation [2] - equation [1] a + 5d - (a + 2d) = 13 - 7 a + 5d - a - 2d = 6 3d = 6 d = 6/3 d = 2 Therefore, common difference = 2 Substitute d = 2 in equation [1] a + 2d = 7 a + 2(2) = 7 a + 4 = 7 a = 7 - 4 a = 3 So, first term = 3
∴ a = 3 , d = 2 |
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