Q. Type the missing numbers in this sequence:52, _____, 70, 79, 88, _____, 106
Identify Sequence Type: Is the given sequence geometric or arithmetic?Here, the difference between consecutive terms is not immediately clear, but we can assume it's an arithmetic sequence since that's a common type of sequence and there are no clear signs of multiplication or division between terms.
Find Common Difference: Find the common difference in the arithmetic sequence.We can use the terms 79 and 88 to find the common difference since they are consecutive terms.88−79=9Common Difference: 9
Find First Missing Number: Find the first missing number in the sequence.If the common difference is 9, we can subtract 9 from 70 to find the missing term before it.70−9=61First Missing Number: 61
Find Second Missing Number: Find the second missing number in the sequence.If the common difference is 9, we can add 9 to 88 to find the missing term after it.88+9=97Second Missing Number: 97
Check Sequence Consistency: Check the sequence with the found missing numbers to ensure it is consistent.The sequence should now be: 52,61,70,79,88,97,106.We can check if the difference between each term is indeed 9.61−52=970−61=979−70=988−79=997−88=9106−97=9All differences are 9, so the sequence is consistent.