Question

which term of the A.P. 27,24,21,......is zero?​

Answer 1

Given

• A.P. = 27, 24, 21, ....

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To find

• The term of the given A.P that is zero.

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Solution

• Here, in the given A.P. we have

⠀⠀⠀⠀⠀⠀❍ First term (a) = 27

⠀⠀⠀⠀⠀⠀❍ Common difference (d) = -3

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• Let the last term $\mathcal\blue{a_n}$ be 0.
• Now, we need to find the term (n).

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★ We know that

$\large{\boxed{\boxed{\sf{a_n = a + (n - 1)d}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a_n = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a + (n - 1)d = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {27 + (n - 1)(-3) = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {(n - 1)(-3) = -27}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n - 1 = \dfrac{-27}{-3}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n - 1 = 9}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n = 9 + 1}$

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$\bf:\implies\: \: \: \: \: \: \: \: {n = 10}$

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Hence,

• The 10th term of the given A.P will be 0.

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