which term of progression 19 18.2 17.4 is the first negative term.​

1 thought on “which term of progression 19 18.2 17.4 is the first negative term.​”

1. Answer :-

   25th term of the given A.P. is the first negative term.​

   Solution :-

   [tex]\lonrightarrow[/tex][tex]\longrightarrow[/tex] The given A.P. is – 19, 18.2, 17.4 ….

   Here,

   The first term (a) = 19

   The difference between two consecutive terms (d) = 18.2 – 19 = 17.4 – 18.2 = -0.8

   [tex]\lonrightarrow[/tex][tex]\longrightarrow[/tex] Let the nth term term of the given A.P. be negative

   Then, [tex]T_n <0[/tex]

   [Using the formula, [tex]T_{n}= a +(n-1)d[/tex]]

   => [a + (n – 1)d] < 0

   => [19 + (n – 1)-0.8] < 0

   => [19 – 0.8 n + 0.8] < 0

   => [19.8 – 0.8 n] < 0

   => – 0.8 n < -19.8

   => 0.8 n > 19.8

   => n > [tex]\dfrac{19.8}{0.8}[/tex]

   => n > 24.75

   => n > 25 [after round -off]

   Therefore, n = 25, i.e., 25th term is the first negative term.​

   [tex]\star[/tex] Checking it –

   [tex]T_{24}[/tex] = 19 + (24 – 1)-0.8 = 19 + (23)-0.8 = 19 – 18.4 = 0.6

   [tex]T_{25}[/tex] = 19 + (25 – 1)-0.8 = 19 + (24)-0.8 = 19 – 19.2 = -0.2

   After checking our answer it is confirmed that 25th term is the first negative term of the A.P. 19, 18.2, 17.4.

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