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Questions
How many terms of the A.P. 21, 18, 15, … must be added to get the sum 0?
How many terms of the A.P. 21, 18, 15,... must be added to get the sum zero?
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Solution
The given AP is 21, 18, 15,……….
Here, a = 21 and d =18 − 21 = − 3
Let the required number of terms be n. Then,
Sn = 0
`⇒ n/2 [ 2 xx 21 + (n − 1) xx (−3) ] = 0` `...[{s_n = n/2 [ 2a +(n − 1) d]}]`
`⇒ n/2 (42 − 3n + 3) = 0`
⇒ n (45 − 3n) = 0
⇒ n = 0 or 45 − 3n = 0
⇒ n = 0 or n = 15
∴ n = 15 (Number of terms cannot be zero)
Hence, the required number of terms is 15.
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