Hello,
Can someone help with these questions please.
Thank you.

1. In the sequence of numbers, 2,3,5,8,12.....
What is the first 3 digit number?

Instead of working it all the way (as it is a test and will take too long) , how do I do this? Is there a formula?

2. How many three digit numbers contain at least 2 sevens?
Again, this type of questions, is there a formula/ technique to work out? Instead of having work through one by one? This is a test question. I think only 1 mark.

Thank you very much.

The first one looks like it's trying to be the Fibonacci sequence - should 12 be 13?

In any case although there is a formula for the nth term that would be of no use here : you need to spot the pattern (add the last two numbers together) and it will grow quite quickly to be a 3 digit number 2,3,5,8,13,21,34,55,89 - the next one is obviously 3 digit without even needing to work it out

The second one: again there is probably a general formula, but expecting a child to remember every possible formula for every possible version of the question is less useful than equipping them with the reasoning skills to work it out from scratch

So one way to do it would be think first:

how many different places can there be NOT a 7 if there are two 7s?

Answer - 3

How many different not-7 digits can go in that place?

Answer - 9 (0,1,2,3,4,5,6,8,9)

Have we missed any - Yes - the number 777

Have we over-counted? Yes - we can't count 077 as it's not a 3 digit number

So the final answer is...... ????

Systematic thinking and pattern-spotting are the skills being looked for

I assumed the 12 was correct and the sequence is the gap between numbers increasing by one each time?
2 to 3 is 1
3 to 5 is 2
5 to 8 is 3
8 to 12 is 4

So the next number is 17, then 23, 30, 38?

_________________
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You're probably right: that would grow more slowly of course and would be two more than the series of triangle numbers 1,3,6,10 etc

But I can't imagine a 10-year old is expected to know the formula for those either - spotting the pattern is the trick, then continuing it far enough (so it's a test of arithmetic)

These are not suitable 11+ questions ... where do they come from?

They look more like the sort of thing found in the Maths Challenge

Hi solimum and toadmum,
Thank you for taking time to reply.
Yes, the sequence is indeed 2,3,5,8,12..( the last number is a 12).
The answer is given as 107.

This is given from a tuition centre. Question taken from a Manchester Grammar school paper. So it is for an independent school exam. Thanks for telling me that it is not suitable for 11 plus; however I'm more interested in how to learn to solve this, instead of knowing whether it is suitable for 11 plus, as it comes from an independent school paper

Private schools should not be setting 11+ questions that are not in the primary NC - it is outrageous.

Look at https://nrich.maths.org/primary for more games & activities aimed at encouraging mathematical thinking.