Question

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

Answer 1

Answer:

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

Answer 2

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,

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

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

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

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

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

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

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

$\rm \implies\:n > 22.66$

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

So, Option (b) is correct.

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Learn More :

↝ 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.