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All the terms of an AP are natural numbe...

All the terms of an AP are natural numbers and the sum of the first 20 terms is greater than 1072 and less than 1162.If the sixth term is 32, then

A

first term is 7

B

first term is 12

C

common difference is 4

D

common difference is 5

Text Solution

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The correct Answer is:
A, D
Let the AP start with n and common differencem, then according to question,
`n+5d=32`
`n=32-5d " " "…..(i)"`
and `1072ltn+(n+d)+"……."+(n+19d)lt1162`
`1072lt20n+(19xx20)/(2)dlt1162`
`1072lt640-100d+190dlt1162`
`432lt90dlt522`
`4.8ltdlt5.8`
Let d is natutal number, so `d=5`
`:.n=32-5xx5=7`
First term is 7 and common difference is 5.
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