Question

*समांतर श्रेणी 4, 9, 14, ___________ 254 के a₈ - a₄ का मान क्या होगा?*

1️⃣ 18
2️⃣ 14
3️⃣ 20
4️⃣ 11​

Answer 1

Answer:

3)20

Step-by-step explanation:

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Answer 2

Given:

समांतर श्रेणी 4, 9, 14, ___________ 254 के a₈ - a₄ का मान क्या होगा?

Solution:

Know that,

$\[{a_n} = a + \left( {n - 1} \right)d\]$

Where $a$ is the first term, $n$ is the number of term and d is the common difference.

Find the common difference,

$\[\begin{array}{l} \Rightarrow d = {a_2} - {a_1}\\ \Rightarrow a = 9 - 4\\ \Rightarrow a = 5\end{array}\]$

Now find $\[{a_8}\]$,

$\[\begin{array}{l} \Rightarrow {a_8} = 4 + \left( {8 - 1} \right) \times 5\\ \Rightarrow {a_8} = 4 + 7 \times 5\\ \Rightarrow {a_8} = 4 + 35\\ \Rightarrow {a_8} = 39\end{array}\]$

Find $\[{a_4}\]$,

$\[\begin{array}{l} \Rightarrow {a_4} = 4 + \left( {4 - 1} \right) \times 5\\ \Rightarrow {a_4} = 4 + 3 \times 5\\ \Rightarrow {a_4} = 4 + 15\\ \Rightarrow {a_4} = 19\end{array}\]$

Evaluate $\[{a_8} - {a_4}\]$,

$\[\begin{array}{l} \Rightarrow {a_8} - {a_4} = 39 - 19\\ \Rightarrow {a_8} - {a_4} = 20\end{array}\]$

Hence the value of $\[{a_8} - {a_4}\]$ is 20.