Question

If nth term of an A.P is 2n then the sum of first n terms of the A.P is
a.n²
b.n(n + 1)
c.n(n + 2)
d.n2 + 2n​

Answer 1

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✳If nth term of an A.P is 2n then the sum of first n terms of the A.P is

a.n²

b.n(n + 1)

c.n(n + 2)

d.n2 + 2n

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✒Option B n(n+1)

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✳GIVEN...

✏The nth term of an AP = 2n

✳TO FIND...

✏Sum of n terms...?

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$\large{ \sf{ \leadsto{ \color{blue}{u \: must \: know...}}}} \\ \\ \large{ \sf{ \star{ formula \: for \: \: nth \: term \: of \: ap...}}} \\ \huge{ \bold{ \boxed{ \sf{ \green{ \red{a}n = a + (n - 1)d}}}}} \\ \\ \large{ \sf{ \red{a}n = nth \: term \: of \: ap}} \\ \\ \large{ \sf{a = first \: term \: of \: ap}} \\ \\ \large{ \sf{n = \: no. \: of \: terms}} \\ \\ \large{ \sf{ d = common \: difference}}$

$\large{ \sf{ \leadsto{ \purple{ by \: using \: formula...}}}} \\ \\ \large{ \sf{ \implies{ \red{a}n = 2n}}} \\ \\ \large{ \sf{ \red{putting \: n = 1 \: \: 2 \: \: 3....}}} \\ \\ \large{ \sf{ \implies{ \red{a}1 = 2}}} \\ \large{ \sf{first \: term = 2}} \\ \\ \large{ \sf{ \implies{ \red{a}2 = 4}}} \\ \large{ \sf{ \red{a}2 = \red{a}1 + (2 - 1)d}} \\ \large{ \sf{ \implies{4 = 2 + d}}} \\ \large{ \sf{ common \: difference = 2}}$

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$\large{ \sf{ \leadsto{ \color{blue}{ u \: must \: know..}}}} \\ \\ \large{ \sf{ \star{formula \: for \: sum \: of \: n \: terms}}} \\ \\ \huge{ \sf{ \boxed{ \green{ \red{s}n = \frac{n}{2} 〖2a + (n - 1)d〗}}}} \\ \\ \large{ \sf{ \red{s}n = sum \: of \: n \: terms}}$

$\large{ \sf{ \leadsto{ \color{blue}{ by \: using \: this \: formula...}}}} \\ \\ \large{ \sf{ \implies{ \red{s}n = \frac{n}{2} 〖2 \times 2 + (n - 1)2〗}}} \\ \\ \large{ \sf{ \implies{ \red{s}n = \frac{n}{2} 〖4 + 2n - 2〗}}} \\ \\ \large{ \sf{ \implies{ \red{s}n = \frac{n}{ \cancel{2}} \times \cancel{ 2}(1 + n)}}} \\ \\ \large{ \sf{ \implies{ \red{s}n = {n}^{2} + n}}} \\ \\ \large{ \sf{ \implies{ \purple{ \boxed{ \red{s}n = n(n + 1)}}}}}$

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$\large{ \bold{ \green{ \underline{required \: answer \: is \: n(n + 1)}}}}$