How many terms in A.P. 18,16,14--------- must be taken so that their sums is zero.
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Answer:
19 terms must be taken so that the sum is zero
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Given:-
- A.P. 18,16,14---------
- Sum = 0
To find:-
- Find the nth term of an Ap.?
Solutions:-
- First term (a) = 18
- Common difference (d) = a2 - a1 = 16 - 18 = -2
- Let the number of terms of an Ap be 'n'
According to the questions;
=> l = a + (n - 1)d
=> l = 18 + (n - 1)(-2)
=> l = 18 - 2n + 2
=> l = 20 - 2n ..........(i)
Sn = n/2[a + l]
=> 0 = n/2 × [18 + 20 - 2n] (using Eq ...(i)....)
=> 0 = n/2 × [38 - 2n]
=> 0 = n/2 × 2[19 - n]
=> 0 = n[19 - n]
=> 0 = 19n - n²
=> n² = 19n
=> n = 19
Hence, the nth terms of an Ap is 19.
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