Which term of the AP 24 21. 18.15.Is the first negative term

1.	Which term of the AP 24 21. 18.15.Is the first negative term
Answer» $\large\underline{\sf{Solution-}}$ $\rm :\longmapsto\:Let \: assume \: that \: a_n \: is \: the \: first \: negative \: term.$ GIVEN AP series is 24, 21, 18, 15, ---- So, First term of an AP, a = 24 Common DIFFERENCE, d = 21 - 24 = - 3 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. As, $\rm :\longmapsto\:a_n < 0$ On substituting the values, we get $\rm :\longmapsto\:a + (n - 1)d < 0$ $\rm :\longmapsto\:24 + (n - 1)( - 3) < 0$ $\rm :\longmapsto\:24 - 3n + 3 < 0$ $\rm :\longmapsto\:27 - 3n< 0$ $\rm :\longmapsto\:27 < 3n$ $\rm :\longmapsto\:9 < n$ $\bf\implies \:n > 9$ $\bf\implies \:n = 10, \: 11, \: 12, \: - - - -$ Hence, 10TH term is the first negative term. Additional Information :- SUM of n terms of an AP is given by $\: \: \: \: \: \boxed{ \bf \: S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}$ Wʜᴇʀᴇ, Sₙ is the sum of n terms. a is the first term of the sequence. n is the no. of terms. d is the common difference.

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