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Question
How many terms of the AP 21, 18, 15, … must be added to get the sum 0?
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Solution
Thee given AP is 21, 18, 15,……….
Here, a = 21and d =18- 21 = - 3
Let the required number of terms be n. Then,
`s_n = 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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