7. In the arithmetic sequence 1, 5, 9, 13, .., which term is 405? * О 102 O 101 О 100 О 9

Q: How many integers between 100 and 400 contain the digot 2?

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Q: 2. (4 points) Verify that 223 is a prime number. Show your work and explain your reasoning.

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Q: low many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if…

A: To find the number of different sequences of 4 digits following the given conditions, we can…

Q: What is the most probable next number in the sequence?…

A: Given sequence is 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ...

Q: The numbers in the sequence 1,3,6,10,15,21… are called as triangular numbers. Determine the 15th…

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Q: 2 letter sequences can be formed from the 8 letters in theword “sequence”?

A: Given, A letter = [ s,e,q,u,e,n,c,e] Number of letters = 8 By using  permutation and combination,…

Q: 4. One way to add up n natural numbers can be described as: ("+1) which is in 'combinations' form.…

A: Generally sum of n natural numbers by using combinations we can find them using n+1c2. By using this…

Q: how many sequences of 2n letters can be formed using n distinct symbols if each symbol is used…

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Q: A four-bit code word is any sequence of four digits, where each digit is either a 0 or a 1. For…

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Q: a) How many area codes were possible with this arrangement? How many telephone numbers does the…

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Q: How many 4-digit numbers can be formed from 0, 1, 3, 5, 7, & 9 if repetition of digits is NOT…

A: Solution-: How many 4-digit numbers can be formed from 0,1,3,5,7 and 9 if repetition of digits is…

Q: fill the missing number between 9 and 5 in the sequence3,5,9_,15,23,33

A: The objective is to fill the missing number between 9 and 15 in the sequence  3, 5, 9 ,__, 15, 23,…

Q: which decimals are rational numbers? select all that apply.

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Q: Mario claims that if the denominator of a fraction I5 a decimal. Do you agree? Use an example to…

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Q: Which of these gives the prime numbers between 0 and 7? (A) 0,1,2,3,4,5,6,7 (B) 1,2,3,4,5,6…

A: A number is called prime number if it is divisible only by 1 and itself.  Note- 1 is not a prime…

Q: How many different sequences of 5 ternary digits (0, 1, 2) are possible? The number of different…

A: There are total 3 choices for each digit. We will have to pick 5 digits. Each digit can be picked in…

Q: 9. Leila was studying number patterns. a) Write down the missing terms in the following sequence:…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: How many numbers between 3000 and 6000 can be formed from the digits 0, 1, 2, 3, 4, 5, 6 if…

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Q: How many numbers between 3000 and 4000, with distinct digits, can be formed using the    digits 1,…

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Q: How many five​-digit numbers can be formed with the first two digits odd and the last three digits…

A: The number of digits need to be formed is five. The first two digits are odd and the last three…

Q: a code word is either a sequence of three letters followed by two by two digits or two letters…

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Q: Add the numbers in the series 3+11+19+27+..._395+403.

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Q: If the sum of a certain number of terms starting from first term of an AP is 25,22,19,,,....,,is 116…

A: A.P is of the form 25,22,19, ... Here first term =a = 25 Common Difference = d = 22-25 = -3 Sum of n…

Q: 11. What is the sum of all 4 digit numbers formed using the digits 2, 3,4 and 5 without repetition?

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Q: Until recently, all area codes had a 0 or a 1 as the middle digit and the first digit could not be 0…

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Q: a) Write down the missing terms in the following sequence: 13, 17, 21, 29, 37, - b) She continues…

A: The general form of an Arithmetic Progression(AP) is a, a + d, a + 2d, a + 3d where 'a' is the first…

Q: Suppose that 6 machines can complete a certain task in 9 days. If there are 18 machines, how many…

A: Concept: If number of machine increase then number of work completion day will decrease . Hence Both…

Q: The sum of five consecutive natural numbers is 145. What is the middle of these numbers? О 28 О 27 O…

A: Given sum of five consecutive numbers is  145 We can assume that  five numbers are n,n+1,n+2,n+3,n+4…

Q: Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be…

A: Given problem Given that   Assuming that any arrangement of letters forms a 'word', how many…

Q: What 3-digit number has the number 5 as its digit in the tens place and the digit in the hundreds…

A: The digit in the tens place is 5. Consider the number is x5y. The digit of the hundreds place is…

Q: 8.How many 2 digit even number can be formed from the digit 1,2,3,4,5 if the digits can't be…

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Q: How many integers between 100 and 400 contain the digit 2? There are integers between 100 and 400…

A: Numbers between 200 and 299 contains 2 So total integers = 100 Numbers between 120 – 129 contains 2…