Question

In an A.P, given a=7, a13=35, find S13​

Answer 1

$\ S13 = 273$

Refer the attachment

Answer 2

$\large\underline{\bf Given} :$

• a = 7
• a₁₃ = 35

$\large\underline{\bf To \: Find} :$

• S₁₃ = ?

$\large\underline{\bf Solution} :$

We have :

• a = 7
• a₁₃ = 35

To find S₁₃, we have a formula :

$\underline{\boxed{\sf S_n = \dfrac{n}{2} (a + a_n )}}$

$\sf : \implies S_{13} = \dfrac{13}{2} (a + a_{13} )$

By substituting values :

$\sf : \implies S_{13} = \dfrac{13}{2} (7 + 35)$

$\sf : \implies S_{13} = \dfrac{13}{2} \times 42$

$\sf : \implies S_{13} = \cancel{\dfrac{546}{2}}$

$\sf : \implies S_{13} = 273$

$\: \: \: \: \: \underline{\boxed{\sf S_{13} = 273}}$

Hence, value of S₁₃ is 273.