Question

25. Which term of the AP 20, 77/4, 37/2,71/4.... is its first
is its first negative term?
[CBSE 2017]​

Answer 1

✬ Term = 28th ✬

Step-by-step explanation:

Given:

• A.P series is 20 , 77/4 , 37/2, 71/4....

To Find:

• Which term of AP will be its first negative term ?

Solution: Let aⁿ be the first negative term of this AP.

Here in this AP series we have

➟ a (first term) = 20

➟ d (common difference) = 77/4 – 20

➟ d = 77 – 80/4 = –3/4

As we know that nth term of AP us given by

★ aⁿ = a + (n – 1)d ★

A/q

• Term should be negative therefore

$\implies{\rm }$ a + (n – 1)d < 0

$\implies{\rm }$ 20 + (n – 1) × –3/4 < 0

$\implies{\rm }$ 20 + (–3n + 3/4) < 0

$\implies{\rm }$ 20 – 3n/4 + 3/4 < 0

$\implies{\rm }$ 20 + 3/4 < 3/4n

$\implies{\rm }$ 80 + 3/4 < 3/4n

$\implies{\rm }$ 83/4 < 3/4n

$\implies{\rm }$ n > 83/4 × 3/4

$\implies{\rm }$ n > 83/4 = 27.66

Hence, 28th term will be the first negative term of the given AP series.

Answer 2

Answer:

▶ Term = 27.6 $\approx$ 28.

Step-by-step explanation:

Given that,

AP :- 20 , 77/4 , 37/2 , 71/4,......

Here, a = 20

▶ d = $t_2 - t_1$

▶d = 77/4 - 20

▶d = -3/4

As we know that,

$\bold{a_n}$ = a + (n - 1) d

Given, Term should be negative,

▶a + (n - 1)d < 0

▶20 + (n - 1) × -3/4 < 0

[ Multiply by 4 on both sides, We get ]

▶80 + (n - 1) × -3 < 0

▶80 - 3n + 3 < 0

▶83 - 3n < 0

▶-3n < -83

▶n > 27.6 $\approx$ 28

Hence,

• The 28th term will be the first negative term.