Q. 999) If the 3rd and the 9th terms of an A.P. are 4 and − 8 respec

1.	Q. 999) If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively, then which term of this A.P is zero.
Answer» ${\underline{\boxed{\red{\sf{Given \: that :}}}}}$ $\longrightarrow$ ${\tt{3rd \:term,\: a_3 \:= \:4}}$ $\longrightarrow$ ${\tt{and\: 9th\: term,\: a_9\: =\: -8}}$ ${\underline{\boxed{\green{\sf{Solution :}}}}}$ We know that, the nth term of AP is; $\longrightarrow$ ${\tt{a_n = a + (n -<klux>1</klux>) d}}$ THEREFORE, $\longrightarrow$ ${\tt{a_3 = a + (3 - 1) d}}$ $\longrightarrow$ ${\red{\tt{4 = a + 2d ………… (i)}}}$ $\longrightarrow$ ${\tt{a_9 = a + (9 -1) d}}$ $\longrightarrow$ ${\tt{\green{-8 = a + 8d …………… (ii)}}}$ On subtracting equation (i) from (ii), we will GET here, $\longrightarrow$ ${\tt{-12 = 6d}}$ $\longrightarrow$ ${\boxed{\red{\tt{d = -2}}}}$ From equation (i), we can write, $\longrightarrow$ 4 = a + 2 (−2) $\longrightarrow$ 4 = a − 4 $\longrightarrow$ ${\boxed{\red{\tt{a = 8}}}}$ Let nth term of this A.P. be ZERO. $\longrightarrow$ ${\boxed{\purple{\tt{a_n = a + (n -1) d}}}}$ $\longrightarrow$ 0 = 8 + (n − 1) (−2) $\longrightarrow$ 0 = 8 − 2n + 2 $\longrightarrow$ 2n = 10 $\longrightarrow$ ${\boxed{\blue{\tt{n = 5}}}}$ ${\large{\underline{\red{\tt{Hence, \:5th\: term \:of \:this\: A.P. \:is \:0 .}}}}}$