Question

Which term of AP 24 ,21,18,15........ is first negative term.​

Answer 1

here,

a = 24

d = -3

d is negative so it must be less then 0

a + (n-1)d <0

24+(n-1)-3 <0

24-3n+3 <0

27-3n <0

27 <3n

n>27/3

n>9

the first negative term is must be 10th term....

hope it's helpful for u

Answer 2

$\huge{\boxed{\boxed{\red{\ulcorner{\mid{\overline{\underline{\bf{Answer:-}}}}}\mid}}}}$

$\star \: \: 9nd \: term \: is \: the \: first \: negetive \: term \: of \: the \: given \: a.p$

${\underline {\underline{sol - }}}$

$\star \: a \: = 24. \\ \\ \star \: d = - 3$

$\star \: let \: nth \: term \: an \: of \: the \: ap \: be \: the \: first \: negetive \: term \: we \: have \: to \: find \: n \: for \: which \: an \: < 0.$

$an = a + (n - 1)d. \\ \\ = 24 + (n - 1) (- 3). \\ \\ = 24 - 3n + 3. \\ \\ = 27 - 3n.$

A/Q

$an < 0. \\ \\ \implies27 - 3n. \\ \\ \implies \: \cancel - 27 = \cancel- 3n. \\ \\ \implies \: 3n = 27. \\ \\ \implies n = \cancel \frac{27}{3} . \\ \\ \implies n = 9.$

Now ,

We can clearly see 9th term of an Ap have first negative term given.

Let's cheak.

$a10 = a + (n - 1)d. \\ \\ = 24 + (10 - 1) (- 3). \\ \\ = 24 - 27. \\ \\ = - 3.$

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