Question

Given A.P : 2, 5, 8, 11, ....
Calculate the sum of the 22 terms of the A.P.
​

Answer 1

Given

• A.P = 2, 5, 8, 11, ....

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To find

• Sum of 22 terms of the given A.P.

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Solution

• We have an A.P with

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$\tt\longrightarrow{First\: term (a) = 2}$

$\tt\longrightarrow{Common\: difference (d) = 3}$

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As we need to find the sum of 22 terms, so

$\tt\longrightarrow{Number\: of\: terms (n) = 22}$

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Using\: Formula}}}$

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$\: \: \: \: \: \: \: \: \: \: \boxed{\bf{\bigstar{S_n = \dfrac{n}{2} \bigg\lgroup 2a + (n - 1)d \bigg\rgroup{\bigstar}}}}$

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• Putting the values

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$\tt:\implies\: \: \: \: \: \: \: \: {S_{22} = \dfrac{22}{2} \bigg\lgroup 2(2) + (22 - 1) \times 3 \bigg\rgroup}$

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$\tt:\implies\: \: \: \: \: \: \: \: {S_{22} = 11 \bigg\lgroup 4 + (21 \times 3) \bigg\rgroup}$

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$\tt:\implies\: \: \: \: \: \: \: \: {S_{22} = 11 \bigg\lgroup 4 + 63 \bigg\rgroup }$

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$\tt:\implies\: \: \: \: \: \: \: \: {S_{22} = 11 \times 67}$

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$\frak:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{S_{22} = 737}}}}$

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Hence,

• The required sum of the given A.P is 737.