Find the missing number. 2,7,12,17, b.

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Given the sequence: 2,7,12,17, b.

We need to determine the relation between the terms so we can figure out the value of a and b.

We notice that the difference between the consecutive terms 2 and 7 is 5.

Also, the difference between the consecutive terms 12 and 17 is 5 too.

Then we can conclude that we have an arithmetical progression with the common difference between the terms is r= 5.

==> a1= 2

==> a2 =2 + r = 2+ 5 = 7.

==> a3= 2+ 2r = 2+ 10 = 12

==> a4= 2+ 3r = 2+ 15 = 17

==> a5= 2+ 4r = 2+ 20 = 22.

**==> 2, 7, 12, 17, 22 are terms of an A.P where the first terms is 2 and common difference if 5.**

**==> b= 22.**

We are given the series 2,7,a,12,17, b and we have to find a and b.

Now, we can see that 7-2 = 5 and 17- 12 = 5.

Therefore this is an arithmetic progression with the first term 2 and the common difference 5.

The difference between a and 7 has to be 5

=> a - 7 = 5

=> a = 5 +7

=> a = 12

Again, the difference between b and 17 has to be 5

=> b - 17 = 5

=> b = 17 + 5

=> b = 22

**So the required values of a and b are 12 and 22.**

We notice that each term from the given series could be obtained by adding the constant amount 5 to the previous term.

Let's start with the 2nd term 7:

7 = 2 + 5

12 = 7 + 5

17 = 12 + 5

This tells us that b is the next term in the given series, that can be obtained by adding the constant amount 5, to the previous term 17.

b = 17 + 5

**b = 22**

**As we can see, the given series is an arithmetic series, whose common difference is d = 5.**

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