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The sum of the first 5 terms and the sum...

The sum of the first 5 terms and the sum of the first 10 terms of an AP are same.Which one of the following is the correct statement? (a) The first term must be negative (b) The common difference must be negative (c) Either the first term or the common difference is negative but not both (d) Both the first term and the common difference are negative

Text Solution

Verified by Experts

`S_5=5/2(2a+(5-1)d)=5/2(2a+4d)-(1)`
`S_10=10/2[2a+(10-1)d]=5(2a+9d)-(2)`
`S_5=S_10`
`5/2(2a+4d)=5(2a+9d)`
`2a+4d=4a+18d`
`2a+14d=0`
`a=-7d`
option C is correct.
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