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icang [17]
2 years ago
12

The negative term of the sequence 65, 62, 59 is(a) 22(b) 23(c) 24(d) 27​

Mathematics
2 answers:
andrew11 [14]2 years ago
3 0

Answer:

22,23,24,27.....lol...

kondor19780726 [428]2 years ago
3 0

Step-by-step explanation:

\large\underline{\sf{Solution-}}

Given series is

\rm :\longmapsto\:65, \: 62, \: 59, \:  -  -  -  -

Since, its an AP series with

First term, a = 65

Common difference, d = - 3

Let assume that nth term of the series be first negative term.

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}

Wʜᴇʀᴇ,

aₙ is the nᵗʰ term.

a is the first term of the sequence.

n is the no. of terms.

d is the common difference.

Tʜᴜs,

\red{\rm :\longmapsto\:a_n < 0}

\rm :\longmapsto\:a + (n - 1)d < 0

\rm :\longmapsto\:65+ (n - 1)( - 3) < 0

\rm :\longmapsto\:65 - 3n + 3 < 0

\rm :\longmapsto\:68 - 3n < 0

\rm :\longmapsto\:- 3n <  - 68

\rm \implies\:n > \dfrac{68}{3}

\rm \implies\:n > 22.66

\bf\implies \: {23}^{rd}  \: term \: is \: first \: negative \: term.

<em>So, Option (b) is correct. </em>

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

<h2>Learn More :</h2>

↝ Sum of n  terms of an arithmetic sequence is,

\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}

Wʜᴇʀᴇ,

Sₙ is the sum of n terms of AP.

a is the first term of the sequence.

n is the no. of terms.

d is the common difference.

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