Question

इंसर्ट 10 रेशनल नंबर बिटवीन - 2 अपऑन 3 एंड 9 अपऑन 13​

Answer 1

Step-by-step explanation:

Given :

•First term (a) → 2

• Sum of first 5 terms = ¼[ Sum of next five terms ]

Using the formula for Sum of n terms :

= > S_n = \frac{n}{2} [2a + (n - 1)d \: ]=>S

n

=

2

n

[2a+(n−1)d]

For Sum of first five terms ,

\begin{lgathered}= > \: S_5 = \frac{5}{2} [ \: 2 \times 2 + (5 - 1)d \: ] \\ \\ = > \: S_5 = \frac{5}{2} \: \: [ 4 + 4d] \\ \\ = > \: S_5 = \frac{5}{2} \times 4 \: \: [ 1+ d] \\ \\ { \bold{S_5 = 10[1 + d]}}\end{lgathered}

=>S

5

=

2

5

[2×2+(5−1)d]

=>S

5

=

2

5

[4+4d]

=>S

5

=

2

5

×4[1+d]

S

5

=10[1+d]

For the Sum of first 10 terms ,

\begin{lgathered}= > S10 = \frac{10}{2} [ \: 2 \times 2 + (10 - 1)d \: ] \\ \\ = >{ \bold { S10 = 5 [ 4 + 9d \ ]}}\end{lgathered}

=>S10=

2

10

[2×2+(10−1)d]

=>S10=5[4+9d ]

Now , as per question :

\begin{lgathered}\: S_5 = \frac{1}{4} \: [ \: S10 - \: S_5 \: ] \\ \\ = > 10 + 10d = \frac{1}{4} \: [ \: 20 + 45d \: - 10 - 10d \: ] \\ \\ = > 40 + 40d = 10 + 35d \\ \\ = > 5d = - 30 \\ \\ = > { \boxed{ \bold {d = - 6}}}\end{lgathered}

S

5

=

4

1

[S10−S

5

]

=>10+10d=

4

1

[20+45d−10−10d]

=>40+40d=10+35d

=>5d=−30

=>

d=−6

•°• Sum of first 20 terms :-

\begin{lgathered}= > \: S20 = \frac{20}{2} \: [ \: 2 \times 2 + (20 - 1) - 6 \: ] \\ \\ = > \: S20 = 10 \: (4 + 19 \times ( - 6))\end{lgathered}

=>S20=

2

20

[2×2+(20−1)−6]

=>S20=10(4+19×(−6))

=> S20 = 10 [ 4 - 114 ]

=> S20 = 10 × (-110)

•°• {\underline{\bold{S20 = -1100}}}

S20=−1100

Answer 2

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