Question

1-2+3-4..are in ap then find s30
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Answer 1

$\Huge{\texttt{{{\color{Magenta}{⛄A}}{\red{N}}{\purple{S}}{\pink{W}}{\blue{E}}{\green{R}}{\red{♡}}{\purple{࿐⛄}}{\color{pink}{:}}}}}$

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$\boxed{ \tt \red{1 - 2 + 3 - 4 + ... - 30 = -15}}$

● Explaination:-

$\sf{Given \: sequence \: is }$

$\boxed{ \tt \red{S = 1 - 2 + 3 - 4 + ... -30}}$

$\sf{Let's \: divide \: this \: sequence \: into \: two \: APs \: for \: convenience}$

$\sf{S2 = -2 - 4 - 6 - ... - 30}$

$\sf{For \: 1st \: AP, n = 15, a = 1, l = 29 }$

$\tt \purple{ \longrightarrow \: S1 = \frac{n}{2 (a + l)} }$

$\tt \purple{ \longrightarrow \: S1 = \frac{15}{2} \times (1 + 29)}$

$\tt \purple{ \longrightarrow \: S1 = \frac{15}{2} × 30}$

$\boxed{ \tt{S1 = 225}}$

$\sf{For \: 2nd \: AP, n = 15, a = -2, l = -30 }$

$\tt \purple{ \longrightarrow \: S2 = \frac{n}{2} (a + l)}$

$\tt \purple{ \longrightarrow \: S2 = \frac{15}{2} × (-2-30)}$

$\tt \purple{ \longrightarrow \: S2 = \frac{15}{2} × (-32)}$

$\tt \purple{S2 = -240}$

$\sf{Total \: sum \: is \: given \: by }$

$\tt \orange{S = S1 + S2 = 225 - 240 = -15}$

$\: \: \: \: \: \: \: \: \boxed{ \therefore1 - 2 + 3 - 4 + ... - 30 = -15}$

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