Question

➡What is the sum of the first 10 numbers of the arithmetic sequence 1,2,3,……?

➡Sum of how many terms of this sequence starting from the first is 300?​

NO NEED OF IRRELEVANT ANSWERS ! ​

Answer 1

$\sf \underline \blue{AnswEr:-}$

$\bf \underline \purple{Given:-}$

• a= 1
• d = 1

$\bf \underline \purple{Formula \: \: Used:-}$

$\tt {\boxed{ \red{S_n = \frac{n}{2} \: \times 2a + (n - 1)d}}}$

$\tt \underline \green{Question :}$

What is the sum of the first 10 numbers of the arithmetic sequence 1,2,3,……?

$\tt \underline \green{Soln :}$

$\longmapsto \sf \bold \pink{S_{10} = \frac{10}{2} (2 \times 1 + (10 - 1)1)}$

$\longmapsto \sf \bold \pink{S_{10} = 5(2 + 9)}$

$\longmapsto \sf \bold \pink{S_{10} = 55}$

$\tt \underline \green{Question :}$

Sum of how many terms of this sequence starting from the first is 300?

$\tt \underline \green{Soln :}$

$\tt {\boxed{ \red{S_n = \frac{n}{2} \: \times 2a + (n - 1)d}}}$

$n/2 (2+(n-1)1) = 300$

$n/2 [1-n] = 300$

$n+n^2=600$

$n+n^2-600=0$

Factorisation ,

x = -b ±√b²-4ac/2a

• a = 1
• b=1
• c=-600

→ √b²-4ac

→√(1)²-4*(-600)

→√1+2400

→√2401

→49

x = -1±49/2

x = -1+49/2 , -1-49/2

x= 24 , -25

n cannot be in negative

•°•Sum of 24 th term is 300

Answer 2

Solution :-

(a) The Sum of the First n Terms of Arithmetic Series Formula can be written as,

$\boxed {\bold {S_n = \frac{n}{2} \Big [2a + (n - 1) d \Big ]}}$

Where,

n ⇒ Number of Terms = 10

a ⇒ First Term = 1

d ⇒ Common Difference of AP = 1

Applying the Given Data in the Formula,

$\begin {aligned} S_{10} & = \frac{10}{2} \Big [2 \times 1 + (10 - 1) 1 \Big ]\\\\\\S_{10} & \Rightarrow 5 \Big [2 + 9 \Big ]\\\\\\& \Rightarrow 5 \Big [11 \Big ] = \bold {55} \end {aligned}$

So, the Sum of the First 10 Numbers of the Arithmetic Sequence is 55 . . .

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(b) Sum of 24 Terms of the Arithmetic Sequence 1, 2, 3, 4 . . . is 300

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