Which term of the A.P. 20, 17, 14, ...... is the first negative term?

March 23, 2026Mathematics

ScanSolve AI Answer

March 23, 2026

Answer

$1) 8^{th}$

Step 1: Identify first term and common difference.

The A.P. is $20, 17, 14, \dots$

First term: $a_1 = 20$

Common difference: $d = 17 - 20 = -3$

Step 2: General term formula.

a_n = a_1 + (n-1)d

Substitute $a_1$ and $d$ :

a_n = 20 + (n-1)(-3) = 20 - 3(n-1)

Step 3: Solve for first $a_n < 0$ .

20 - 3(n-1) < 0

20 < 3(n-1)

n-1 > \frac{20}{3} \approx 6.\overline{6}

n > 7.\overline{6}

Smallest integer $n = 8$ .

Step 4: Verify $n=7$ and $n=8$ .

For $n=7$ :

a_7 = 20 - 3(7-1) = 20 - 3(6) = 20 - 18 = 2 > 0

For $n=8$ :

a_8 = 20 - 3(8-1) = 20 - 3(7) = 20 - 21 = -1 < 0

The 8th term is the first negative term.

Answer: 1) 8th

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