QuestionAugust 25, 2025

Find the cardinal number for the set. 8,10,12,ldots ,66 30 60 15 20

Find the cardinal number for the set. 8,10,12,ldots ,66 30 60 15 20
Find the cardinal number for the set. 8,10,12,ldots ,66 30 60 15 20

Solution
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Answer

30 Explanation 1. Identify the sequence The sequence is arithmetic with first term a_1 = 8 and last term a_n = 66, common difference d = 2. 2. Use formula for nth term of arithmetic sequence Formula: a_n = a_1 + (n-1) \cdot d. Solve for n: 66 = 8 + (n-1) \cdot 2. 3. Solve for n Rearrange: 66 - 8 = (n-1) \cdot 2 \Rightarrow 58 = (n-1) \cdot 2 \Rightarrow n-1 = 29 \Rightarrow n = 30.

Explanation

1. Identify the sequence<br /> The sequence is arithmetic with first term $a_1 = 8$ and last term $a_n = 66$, common difference $d = 2$.<br />2. Use formula for nth term of arithmetic sequence<br /> Formula: $a_n = a_1 + (n-1) \cdot d$. Solve for $n$: $66 = 8 + (n-1) \cdot 2$.<br />3. Solve for n<br /> Rearrange: $66 - 8 = (n-1) \cdot 2 \Rightarrow 58 = (n-1) \cdot 2 \Rightarrow n-1 = 29 \Rightarrow n = 30$.
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