Question

. Which term of the progression 20, 192, 183, 17 … is the first negative term? *

Answer 1

Answer:-

Given:

a = 201

d = 192 - 201

→ d = - 9

We have to find the first negative term i.e., The first term which is less than 0.

We know that,

nth term of an AP = a + (n - 1)d

→ 201 + (n - 1)(- 9) ≤ 0

→ 201 - 9n + 9 ≤ 0

→ 210 - 9n ≤ 0

→ 9n ≤ 210

→ n ≤ 23.3

→ n = 23 (Approx.)

Hence, the 23rd term is the first negative term in the given AP.

Answer 2

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{Answer}}}}⋆$

• 23 (Approx)

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{Explanation}}}}⋆$

$\blue{\bold{\underline{\underline{Given}}}}$

• a = 201
• d = 192 - 201 = -9

$\blue{\bold{\underline{\underline{To \: Find}}}}$

• The first negative term

$\blue{\bold{\underline{\underline{Formula}}}}$

${\boxed{\rm{a + (n-1)d}}}$

$\blue{\bold{\underline{\underline{Solution}}}}$

$201 + (n - 1)( - 9)≤0$

$\implies \: 201 - 9n + 9≤0$

$\implies \: 210 - 9n≤0$

$\implies \: - 9n≤210$

$\implies \: n≤23.3$

$\orange{\bold{\underline{\underline{ANSWER}}}}$

• The 23rd term is the first negative term in the given AP.