Question

1) Find the sum of first 130 natural numbers.​

Answer 1

Answer:

a = 1, d = 1, n= 130

Sn = n/2[2a + (n - 1)d)

S130 = 130/2[2*1 + (130 - 1)1]

= 65(2 + 129) = 65*131 = 8515

Answer 2

$\LARGE\textbf{\underline{\underline{Answers :-}}}$

• The first 130 natural numbers are 1 , 2 , 3 , 4 , 5 ......... 130 .

➙ Here :-

• t₁ = 1 .......( a ) .
• d = 1 .
• n = 130 .

➙ Formula :-

$\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{green}{ S_{n} = \cfrac{n}{2}\left[ 2a + ( n - 1 ) d \right] }}}$

• This Formula is used to find the sum of the nᵗʰ terms .

➙ By using this Formula :-

$\large\: \bigstar\textsf\textcolor{orange}{\: \: \: S_{n} = \cfrac{130}{2} \left[ ( 2 × 1 ) + ( 130 - 1 ) × 1 \right] }\\\\\\\large: \: \Longrightarrow\textsf{ = 65 \left[ 2 + 129 × 1 \right] }\\\\\\\large: \: \Longrightarrow\textsf{ = 65 ( 131 ) }\\\\\\\large: \: \Longrightarrow\underline{\boxed{\textsf\textcolor{purple}{ S _ { n } = 8515 }}}$

∴ The sum of the first 130 numbers is 8515 .