SATHEE: Sequences and Series 2 Question 2

Sequences and Series 2 Question 2

2. Let $S_{n}$ denote the sum of the first $n$ terms of an AP. If $S_{4} = 16$ and $S_{6} = - 48$ , then $S_{10}$ is equal to

(2019 Main, 12 April I)

(a) -260

(b) -410

(d) -380

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Answer:

Correct Answer: 2. (c)

Solution:

Given $S_{n}$ denote the sum of the first $n$ terms of an AP.

Let first term and common difference of the AP be ’ $α$ ’ and ’ $d$ ‘, respectively.

$\begin{aligned} ∴ S_{4} = 2 [2 a + 3 d] = 16 \\ ∵ S_{n} = \frac{n}{2} [2 a + (n - 1) d] \\ \Rightarrow 2 a + 3 d = 8 \dots (i) \\ and S_{6} = 3 [2 a + 5 d] = - 48 [given] \\ \Rightarrow 2 a + 5 d = - 16 \end{aligned}$

On subtracting Eq. (i) from Eq. (ii), we get

$\begin{aligned} 2 d & = - 24 \\ \Rightarrow & d & = - 12 \end{aligned}$

So, $2 a = 44$ [put $d = - 12$ in Eq. (i)]

Now, $S_{10} = 5 [2 a + 9 d]$

$= 5 [44 + 9 (- 12)] = 5 [44 - 108]$

$= 5 \times (- 64) = - 320$

Sequences and Series 2 Question 2

2. Let $S_{n}$ denote the sum of the first $n$ terms of an AP. If $S_{4} = 16$ and $S_{6} = - 48$ , then $S_{10}$ is equal to

Answer:

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Sequences and Series 2 Question 2

2. Let Sn denote the sum of the first n terms of an AP. If S4=16 and S6=−48, then S10 is equal to

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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2. Let $S_{n}$ denote the sum of the first $n$ terms of an AP. If $S_{4} = 16$ and $S_{6} = - 48$ , then $S_{10}$ is equal to