Question

2+4+6+8+.............+214=?

Answer 1

$\underline\mathit\blue{Arithmetic\: progression...}$

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2+4+6+8+.............+214

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$\underline\mathit\blue{Given...}$

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nth term = 214

a = 2

d = 2

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$\huge\underline\mathit{SoLution...}$

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✫✫ nth = a + ( n - 1 } × d

214 = 2 + ( n - 1 ) × d

214 = 2 + 2n - 2

214 = 2n

$\dfrac{214}{2}$ = n

• $\boxed{\red{\underline\textbf{107 = n}}}$

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✫✫ So, the total number of the AP be 107...

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✫✫ Sn = $\dfrac{n}{2} (a + l)$

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Since, we know the last term...so, we will use this formula...

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Sn = $\mathit \dfrac{107}{2} (2 + 214)$

Sn = $\mathit \dfrac{107}{2} (216)$

Sn = $\mathit \dfrac{216\times107}{2}$

Sn = $\mathit \dfrac{23112}{2}$

• $\boxed{\red{\underline\textbf{Sn = 11,556}}}$

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Therefore, the sum of Ap will be 11,556...