Question

Which term of
a.p :- 115,110,105,..... will be its first negative term?

Answer 1

Let nth term is a first negative term of given AP .
Tn = a + (n -1)d
here, a is the first term and d is the common difference of AP.
Tn = 115 + (n -1) × (110-115)
Tn = 115 + (n - 1)(-5) < 0
-115 > (n - 1)(-5)
-23 > (n -1)(-1)
n > 24
for negative term n > 24
but if we choose n = 25
then Tn = 115 + (25-1)(-5) = 0
so, first negative term when n = 26
hence, 16th term is first negative term

Answer 2

Answer:

Ur Answer is 25th term

Step-by-step explanation:

$\mathcal \color{red}(GIVEN A.P)$

115,110,105..........

here,

a= 115

d= 110-115= -5

therefore,

$a_{n}$  = a + nd-1d

     = 115-5n+5

$a_{n} = 120- 5n$

but ,

Since we need a negative term ..

therefore

$a_{n}$ < 0

i.e 120-5n <0

     120<5n

     5n>120

       n>24

therefore,

 The first negative term of this A.P is it's 25th term

verification..............

$a_{25}$ = a + (24)d

                          = 115 + (24)-5

                          = 115- 120

                          = -5

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