Question

The second term of an hp is 1 by 6 and its 6th term is -1/
6 then the 20th term is
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Answer 1

Answer:

$t_{2} = 1 \\ t_{6} = \frac{ - 1}{6} \\ t_{n} = a + (n - 1)d \\ t_{2} = a + d \\but \: t_{2} = 1 \\ a + d = 1...(1) \\ t_{6} = a + 5d \\ but \: t_{6} = \frac{ - 1}{6} \\ a + 5d = \frac{ - 1}{6} \\ multipying \: throughout \: by \: 6 \\ 6a + 30d = - 1...(2) \\ multiplying \: eq.(1) \: by \: 6 \\ 6a + 6d = 6...(3) \\ subtracting \: (3) \: from \: (2) \\ we \: get \\ 24d = - 7 \\ d = \frac{ - 7}{24} \\ substituting \: value \: of \: .d. \: in \: (1) \\ a + (\frac{ - 7}{24}) = 1 \\ a - \frac{7}{24} = 1 \\ a = 1 + \frac{7}{24} \\ a = \frac{(24 + 7)}{24} \\ a = \frac{31}{24} \\ a = 1.3 \\ \\ t_{20} = a + 19d \\ \: \: \: \: \: \: \: = 1.3 + ( - 5.5) \\ \: \: \: \: \: \: \: =1.3 - 5.5 \\ \: \: \: \: \: \: \: = </u></em></strong><strong><em><u>-</u></em></strong><strong><em><u>0.24 \\ t_{20} = \frac{</u></em></strong><strong><em><u>-</u></em></strong><strong><em><u>24}{100}$

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