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Type the missing numbers in this sequence: $\newline$ $34$ , $\_$ , $52$ , $61$ , $70$ , $\_$ , $88$

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Arithmetic sequences

Full solution

Q. Type the missing numbers in this sequence:

\newline

34

,

\_

,

52

,

61

,

70

,

\_

,

88

Identify Pattern: First, let's look at the sequence to determine if there is a pattern that we can identify. We have the numbers $34$ , $52$ , $61$ , $70$ , and $88$ . We need to find the difference between the consecutive numbers to see if there is a consistent increase.
Calculate Difference $1$ : Calculate the difference between $52$ and $34$ . $\newline$ $52 - 34 = 18$
Calculate Difference $2$ : Calculate the difference between $61$ and $52$ . $\newline$ $61 - 52 = 9$ $\newline$ This is not consistent with the previous difference. We may need to look at the differences between the other numbers to find a pattern.
Calculate Difference $3$ : Calculate the difference between $70$ and $61$ . $\newline$ $70 - 61 = 9$ $\newline$ This is consistent with the difference between $61$ and $52$ , suggesting that the sequence might be increasing by $9$ after $52$ .
Calculate Difference $4$ : Calculate the difference between $88$ and $70$ . $\newline$ $88 - 70 = 18$ $\newline$ This is consistent with the difference between $52$ and $34$ , suggesting that the sequence might be alternating between increasing by $18$ and $9$ .
Find Missing Number $1$ : Assuming the pattern of increasing by $18$ and then by $9$ alternately, let's find the missing number between $34$ and $52$ . Since the sequence increased by $18$ to get to $52$ , it should increase by $9$ before that. $\newline$ $52 - 9 = 43$ $\newline$ So, the missing number after $34$ should be $43$ .
Find Missing Number $2$ : Now, let's find the missing number after $70$ . Since the sequence increased by $9$ to get to $70$ , it should increase by $18$ next. $\newline$ $70 + 18 = 88$ $\newline$ So, the missing number after $70$ should be $88$ , but we already have $88$ at the end of the sequence. This indicates a mistake in our pattern assumption.

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