Question

1. Show that the numbers 4, 7, 10, 13, 16.......... form an A.P. Find its :
(i) nth term
(ii) 14th term.​

Answer 1

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Answer 2

Step-by-step explanation:

$\sf Given\:sequence\: => 4 , 7 , 10 , ... \\ \\ \sf Here\: t_{1} = a = 4 \: \: \: \: \: t_{2} = 7 \: \: \: \: t_{3} = 10 \\ \\ \sf t_{2} - t_{1} = 7 - 4 = 3 \\ \sf t_{3} - t_{2} = 10 - 7 = 3 \\ \\ \sf Hence\:the\:given\: sequence\:is\:A.P\:with \: a = 4\:and\:d = 3 \\ \\ \sf t_{n} = a + ( n - 1 )d \\ \\ \sf t_{n} = 4 + ( n - 1 )3 \\ \\ \sf t_{n} = 4 + 3n - 3 \\ \\ \sf t_{n} = 3n + 1 \\ \\ \sf t_{14} = 3 (14) + 1 \\ \\ \sf t_{14} = 42 + 1 \\ \\ \sf t_{14} =43$

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