hoe can we get the first negativ e term of an ap like 20, 19*1/4, 18*1/2, ......................... and the term
Asked by | 16th Dec, 2012, 10:30: PM
Expert Answer:
The given A.P is 20, 19 (1/4), 18 (1/2), 17 (3/4),......
Hence, a = 20
d = 19 (1/4) - 20 = -(3/4)
Let the nth term of the A.P be the first negative term. Then,
an < 0
=> a + (n - 1) d
=> 20 + (n - 1) (-3/4) < 0
=> 20 < (n - 1) (3/4)
=> (n - 1) (3/4) > 20
=> (n - 1) > 20/ (3/4)
=> (n - 1) > 20 x 4/3
=> (n - 1) > 80/3
=> n > 80/3 + 1
=> n > (80 + 3)/3
=> n > 83/ 3
=> n > 27 (2/3)
Least integral value of n = 28. Hence, 28nd term of the given A.P is the first negative term .
The given A.P is 20, 19 (1/4), 18 (1/2), 17 (3/4),......
Hence, a = 20
d = 19 (1/4) - 20 = -(3/4)
Let the nth term of the A.P be the first negative term. Then,
an < 0
=> a + (n - 1) d
=> 20 + (n - 1) (-3/4) < 0
=> 20 < (n - 1) (3/4)
=> (n - 1) (3/4) > 20
=> (n - 1) > 20/ (3/4)
=> (n - 1) > 20 x 4/3
=> (n - 1) > 80/3
=> n > 80/3 + 1
=> n > (80 + 3)/3
=> n > 83/ 3
=> n > 27 (2/3)
Least integral value of n = 28. Hence, 28nd term of the given A.P is the first negative term .
Answered by | 18th Dec, 2012, 10:08: AM
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