Question

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

Answer 1

Answer :-

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

Solution :-

$\lonrightarrow$$\longrightarrow$ 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

$\lonrightarrow$$\longrightarrow$ Let the nth term term of the given A.P. be negative

Then, $T_n <0$

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

=> [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 > $\dfrac{19.8}{0.8}$

=> n > 24.75

=> n > 25 [after round -off]

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

$\star$ Checking it -

$T_{24}$ = 19 + (24 - 1)-0.8 = 19 + (23)-0.8 = 19 - 18.4 = 0.6

$T_{25}$ = 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.