Question

what is sum of all odd integers between 2 and 1000 which are divisible by 3??​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$Odd \: \: integers \: \: between \: \: 2 \: \: and \: \: 1000 \\ which \: \: are \: \: divisible \: \: by \: \: 3 \: \: are : \\ 3, \: 9, \: ..........., \: 993, \: 999. \\ Here, \\ a = 3 \\ d = 9 - 3 = 6 \\ T_{n} = 999 \\ n = ? \\ \\ T_{n} = a + (n - 1)d \\ 999 = 3 + (n - 1)6 \\ 999 = 3 + 6n - 6 \\ 999 = 6n - 3 \\ 999 + 3 = 6n\\ \frac{1002}{6} = n \\ \boxed{ \underline{ \underline{ \bf 167}} = n} \\ \\ Sum \: \: of \: \: odd \: \: integers \: \: are : \\ S_{n} = \frac{n}{2} \{2a + (n - 1)d \} \\ S_{167} = \frac{167}{2} \{2 \times 3 + (167 - 1)6 \} \\ S_{167} = \frac{167}{2} \{6 + (166)6 \} \\ S_{167} = \frac{167}{2} \{6 + 996 \} \\ S_{167} = 167 \times 1002 \\ S_{167} = \frac{167}{ \cancel 2_{ \: 1}} \times \cancel{ 1002} _{ \: \: 501} \\ S_{167} = 167 \times 501 \\ \boxed{ S_{167} = \underline{ \underline{ \bf 83667}}}$