Question

If the sum of second and tenth terms of aritmetic sequence is equal to 12, find sum of fourth, sixth and eight terms.​

Answer 1

Answer:

18

Step-by-step explanation:

explanation in image pinned.

Answer 2

Given: sum of second and tenth terms of arithmetic sequence is equal to 12.

To find: Find the sum of fourth, sixth, and eighth terms.​

Solution:

Understand that,

$\[\begin{array}{l}{t_2} = a + \left( {2 - 1} \right)d\\ \Rightarrow {t_2} = a + d\\{t_{10}} = a + 9d\end{array}\]$

Know that from the question,

$\[{t_2} + {t_{10}} = 12\]$

$\[\begin{array}{l} \Rightarrow a + d + a + 9d = 12\\ \Rightarrow 2a + 10d = 12\\ \Rightarrow a + 5d = 6\end{array}\]$

Find the sum of fourth, sixth, and eighth terms i.e., $\[{t_4} + {t_6} + {t_8}\]$.

​Understand that,

Hence, the sum of fourth, sixth, and eighth terms i.e., $\[{t_4} + {t_6} + {t_8}\]$ is 18.