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The sum of the first 5term …

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The sum of the first 5term and the term of first term of AP is 167. It is the sum the first 10th term of this AP is 235 then find the sum of its first twenty term

    • Posted by Archita Chandak 6 years, 8 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 8 months ago

     According to the question, S5 + S7 = 167
    {tex}\Rightarrow \frac{5}{2}[2 a+4 d]+\frac{7}{2}{/tex}[ 2a + 6d] = 167
    {tex}\Rightarrow{/tex} 5(a + 2d) + 7(a + 3d) = 167
    {tex}\Rightarrow{/tex} 12a + 31d = 167 ......(i)
    and S10 = 235
    {tex}\Rightarrow \quad \frac{10}{2}{/tex}[2a + 9d] = 235
    {tex}\Rightarrow{/tex} 2a + 9d = {tex}\frac{235}{5}{/tex} = 47 ........(ii)
    Multiplying eq. (ii) by 6 and then subtracting from (i), we have

    d = {tex}\frac{-115}{-23}{/tex} = 5
    From (ii), we get
    2a + 9d = 47
    {tex}\Rightarrow{/tex} 2a + 9(5) = 47
    {tex}\Rightarrow{/tex} 2a = 47 - 45
    {tex}\Rightarrow{/tex} 2a = 2 {tex}\Rightarrow{/tex} a = 1
    Hence, S20 = {tex}\frac{20}{2}{/tex}[ 2a + 19d]
    = 10[2(1) + 19(5)] = 10[2 + 95] = 970

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    Posted by Hari Anand 9 months, 3 weeks ago

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