Question

Which term of the sequence 114 , 109 , 104 , .............. is the first negative term ?

Answer 1

answer back if correct

Answer 2

hi!
$here \: is \: your \: \: answer$
114 , 109 , 104 , ............ is the sequence.

here,
t2 - t1 = t3 - t2 = -5


The difference between two consecutive terms is constant, thus it is an Arithmetic Progression(A.P)

a = 114 ; d = -5

We know that,

$tn = a + (n - 1)d$
$tn = 114 + (n - 1) (- 5)$

$tn = 114 - 5n + 5$

$tn = 119 - 5n...............(1)$

Here,
The nth term is negative .

so,

$tn < 0$

$119 - 5n < 0...........from(1)$

$119 < 5n$

$\frac{119}{5} < n$

$23.80 < n$

$n = > 24$
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VERIFICATION:

Put n = 24 in the nth term of the A.P

tn = 119 - 5n..........................[from(1)
tn = 119 - 5(24)
tn = 119 - 120
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tn = -1
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Hence verified !
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Therefore,
The 24th term of the given A.P is the first negative term
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$hope \: \: this \: \: helps..$