Question

4. -500 ਤੋਂ 500 ਤੱਕ ਸਾਰੀਆਂ ਸੰਪੂਰਨ ਸੰਖਿਆਵਾਂ
ਦਾ ਜੋੜ ਕਿੰਨਾਂ ਹੈ? What is Sum of all
integers from -500 to 500? -500 ਦੇ
500 ਰਲ ਜਮੀ ਯੁਸੀਂ ਜਾ ਧੀ ਧਾ ਵੈ?
O (a) 0
O (b) 1000
(c) 500
O (d) -500​

Answer 1

Answer:

1000 is the correct answer

Answer 2

$Given \: integers \:-500,-499,-498, \ldots ,\\ 500 \: are\: in \: A.P$

$First \:term (a = a_{1}) = -500$

$Common \: difference (d) = a_{2} - a_{1} \\= - 499 - ( -500) \\= -499 + 500 \\= 1$

$\blue{ Given \: n^{th} \:term \:(a_{n}) = 500 }$

$\implies a + ( n - 1)d = 500$

$\implies -500 + ( n - 1 ) \times 1 = 500$

$\implies n - 1 = 500 + 500$

$\implies n = 1000 + 1$

$\implies n = 1001$

$\boxed{ \pink{ Sum \: of \: n \:terms (S_{n}) = \frac{n}{2} ( a + a_{n}) }}$

$Here , n = 1001 , \: a = -500 \: and \: a_{n} = 500$

$S_{1001} = \frac{1001}{2} ( -500 + 500 ) \\= \frac{1001}{2} \times 0 \\= 0$

Therefore.,

$\red{ Sum \: of \: all \:integers \: from \: -500 }\\\red{ to \: 500 } \green { = 0 }$

$Option \: \green { ( a ) } \: is \: correct$

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