Question

If the 7th term of a H.P. is 8 and the 8th term is 7. Then find the 28th term.

Answer 1

Correct Question

• If the 7th term of a A.P. is 8 and the 8th term is 7. Then find the 28th term.

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Given

• 7th term of the A.P = 8
• 8th term of the A.P = 7

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To find

• 28th term of the A.P.

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Solution

• Let us understand clearly.

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We have two terms of the A.P , we want the first term and the common difference of the A.P.

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As we know, we can write

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$\tt\longrightarrow{a_7 = 8}$

$\tt\longrightarrow{a + 6d = 8}$⠀⠀.... [1]

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Similarly,

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$\tt\longrightarrow{a_8 = 7}$

$\tt\longrightarrow{a + 7d = 7}$⠀⠀.... [2]

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Subtracting\: [1]\: from\: [2]}}}$

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$\tt\longmapsto{a + 7d - (a + 6d) = 7 - 8}$

$\tt\longmapsto{\cancel{a} + 7d - \cancel{a} - 6d = -1}$

$\tt\longmapsto{d = -1}$

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Putting\: the\: value\: of\: d\: in\: [1]}}}$

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$\tt\longmapsto{a + 6(-1) = 8}$

$\tt\longmapsto{a = 8 + 6}$

$\tt\longmapsto{a = 14}$

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• Now, we have the first term (a) and common difference (d) of the A.P.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Finding\: 28th\: term}}}$

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\bf{\bigstar{a_n = a + (n - 1)d{\bigstar}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a_{28} = 14 + (28 - 1)(-1)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a_{28} = 14 + 27(-1)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a_{28} = 14 - 27}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a_{28} = -13}$

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Hence,

• 28th term of the A.P is -13.