SATHEE: Sequences and Series 2 Question 6

Sequences and Series 2 Question 6

7. The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24 , then what is the length of its smallest side?

(2017 Adv.)

(a) -153

(b) -133

(d) -135

Show Answer

Answer:

Correct Answer: 7. (c)

Solution:

We have, $S = a_{1} + a_{2} + \dots + a_{30}$

$= 15 [2 a_{1} + 29 d]$

(where $d$ is the common difference)

$∵ S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

and

$\begin{aligned} T & = a_{1} + a_{3} + \dots + a_{29} \\ = \frac{15}{2} [2 a_{1} + 14 \times 2 d)] \end{aligned}$

( $∵$ common difference is $2 d$ )

$\Rightarrow 2 T = 15 [2 a_{1} + 28 d]$

From Eqs. (i) and (ii), we get

$S - 2 T = 15 d = 75 [∵ S - 2 T = 75]$

$\Rightarrow d = 5$

Now, $a_{10} = a_{5} + 5 d$

$= 27 + 25 = 52$

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Sequences and Series 2 Question 6

7. The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24 , then what is the length of its smallest side?

Answer:

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