Question

solve this chapter :progressions​

Answer 1

17)

→ Total Natural Numbers between 200 and 100 = 200 - 100 = 100

Odd Number :- which is not divisible by 2.

So, we can conclude that, Half numbers will be Odd Numbers and Half will be Even Numbers.

Hence,

→ The No. or odd Numbers b/w 100 and 200 = (100/2) = 50 (Option 1) (Ans.)

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18)

→ First Number b/w 1 and 1000 which is divisible by 3 = 3 = a

→ Last Number b/w 1 and 1000 which is divisible by 3 = 999 = l

So,

→ Total Numbers b/w 1 and 1000 which are divisible by 3 = a + (n - 1)d = 999

→ 3 + (n - 1)3 = 999

→ (n - 1)3 = 999 - 3

→ (n - 1) = (996/3)

→ n - 1 = 332

→ n = 333 .

Therefore,

→ Sum of Numbers b/w 1 and 1000 which are divisible by 3 = (n/2)[a + l]

→ Sn = (333/2)[3 + 999]

→ Sn = (333/2) * 1002

→ Sn = 333 * 501

→ Sn = 166,833 (Option 4) (Ans.)

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19)

→ First Number b/w 107 and 253 which are divisible by 5 = 110 = a

→ Last No. = 250 = l

→ common Difference = d = 5

So,

→ An = a + (n - 1)d

→ 250 = 110 + (n - 1)5

→ 250 - 110 = (n - 1)5

→ (140/5) = (n - 1)

→ 28 = n - 1

→ n = 29 .

Therefore,

→ Sum of Numbers b/w 107 and 253 which are divisible by 5 = (n/2)[a + l]

→ Sn = (29/2)[110 + 250]

→ Sn = (29/2) * 360

→ Sn = 29 * 180

→ Sn = 5,220 (Option 1) (Ans.)

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20)

→ Arithmetic Mean = Average of Numbers . = (First No. + second No.) / 2

→ Arithmetic Mean = { 1/2 + 1/3 } / 2

→ Arithmetic Mean = { (3+2)/6 } / 2

→ Arithmetic Mean = (5/6) / 2

→ Arithmetic Mean = 5/(6*2)

→ Arithmetic Mean = 5/12 (Option 2) (Ans.)

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