Question

any AP consists of 50 terms of which 3rd term of an ap is 12 and last term is 106 find the 29th term

Answer 1

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Answer 2

$an \: = \: a + (n - 1)d \\ \\ a3 = a + 2d = 12(eqn \: 1) \\ \\ \\ \\ a50 = a + 49d = 106(eqn \: 2) \\ \\ \\ subtract \: \: (1) \: \: from \: \: (2) \\ \\ \\ 47d = 94 \\ \\ d = \frac{94}{47} = 2 \\ \\ from \: \: (1) \\ \\ a + 2 \times 2 = 12 \\ \\ a = 12 - 4 = 8 \\ \\ a29 = a + 28d \\ \\ = 8 + 28 \times 2 \\ \\ = 8 + 56 \\ \\ = 64$