Question

If the first term of an AP is -5 and the common difference is 2,then the sum of the first 6 terms is____
a)0 (b)5 (c)6 (d)15.​

Answer 1

GivEn:

• First term of AP (a) = - 5

• Common difference (d) = 2

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To find:

• Sum of the first 6 terms?

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SoluTion:

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As we know that,

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$\star\;{\boxed{\sf{\purple{S_n = \dfrac{n}{2}\bigg[2a + (n - 1)d \bigg]}}}}$

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$\bf Here = \begin{cases} & \text{a = - 5} \\ & \text{d = 2 } \\ & \text{n = 6} \end{cases}$

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Therefore,

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$:\implies\sf S_6 = \dfrac{6}{2}\bigg[2a + (6 - 1)d \bigg]$

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$:\implies\sf S_6 = \dfrac{6}{2}\bigg[2 \times -5 + (6 - 1)2 \bigg]$

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$:\implies\sf S_6 = \dfrac{6}{2}\bigg[2 \times -5 + 5 \times 2 \bigg]$

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$:\implies\sf S_6 = \dfrac{ \cancel{6}}{ \cancel{2}}\bigg[-10 + 10 \bigg]$

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$:\implies\sf S_6 = 3 \times 0$

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$:\implies\sf \pink{S_6 = 0}$

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$\therefore$ Hence, the sum of first 6 terms of AP is 0.

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$\begin{lgathered}\boxed{\begin{minipage}{20 em} \sf \displaystyle \bullet a_n=a + (n-1)d \\\\\\ \bullet S_n= \dfrac{n}{2} \left(a + a_n\right) \end{minipage}}\end{lgathered}$

Answer 2

Given ,

First term (a) = -5

Common difference (d) = 2

As we know that , the sum of first n terms of an AP is given by

$\boxed{ \tt{ S_{n} = \frac{n}{2} \{2a + (n - 1)d \}}}$

Thus ,

$\tt \implies S_{6} = \frac{6}{2} \{2( -5) + (6 - 1)2 \}$

$\tt \implies S_{6} = 3 \{ - 10 + 10 \}$

$\tt \implies S_{6} =3 \times 0$

$\tt \implies S_{6} =0$

Hence , the sum of the first 6 terms of given AP is 0