**Vineet wrote a sequence of numbers in which every odd number is 7 less than the previous number, and every even number is 2 more than the previous one. The first term of the sequence is 100. Find the 5th term. [4 MARKS]**

__Question:__**Options:**

: Steps: 3 Marks

Answer: 1 Mark

Given that:

The first term of the sequence = 100.

Now every odd number is 7 less than the previous one and every even number is 2 more than the previous one.

So the second term=100 + 2 = 102

Third term = 102 - 7 = 95

Fourth term = 95 + 2 = 97

Fifth term = 97 - 7 = 90

Hence, the fifth term of the sequence is 90.

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## More Questions on This Topic :

**Find the value of the following, using suitable properties:**

__Question 1.__a) 406×516

b) 8 ×291×125

[3 MARKS]

: Steps: 1×2=2 Marks

Answer: 0.5×2=1 Mark

a)By distributive law 406×516 = (400 + 6)×(500 + 16)

= 200000 + 96 + 6400 + 3000 = 2,09,496 b) By distributive law

8 ×291×125=(4×2)×(290+1)×(25× 5)=(25× 4)×(5×2)×(290+1)

= 100 × 10 × (290+1)= 1000 × (290+1)

= 290000 + 1000 = 291000

**Mahesh found a bicycle in a sale for Rs 2500 but it required a new brake cable and brake oil to make it work perfectly. He bought brake cable for Rs.82 and brake oil for Rs.20, fixed it up and then sold it to his neighbour for Rs. 3500. How much profit did he make on that deal? [4 MARKS]**

__Question 2.__: Steps: 2 Marks

Formula: 1 Mark

Answer: 1 Mark

Mahesh bought a bicycle for Rs. 2500. Repairing cost = Rs. (82 + 20) = 80+2+20 = 100+2 = Rs.102 Total expenses on the bicycle = Rs. (2500 + 102) = 2500+100+2 = 2600+2 = Rs.2602 Profit = (Selling Price - Cost Price) = Rs. (3500 - 2602) = 3500-2600-2 = 900-2 = Rs. 898

**Study the following number patterns:**

__Question 3.__45×9+2=407

456×9+3=4107

4567×9+4=41107

Find the next 2 lines.

[4 MARKS]

: Application: 2 Marks

Steps: 1 Mark

Answer: 1 Mark

This pattern is like this:- 45×9+2=407 456×9+3=4107 4567×9+4=41107 For next three lines, it would be like this-

As we can see in the pattern, the number of digits is incremented by 1, and the units digit is the successor of the previous number.

Also, the number which we are adding to the product is incremented by 1.

Using distributive property we can make the calculations simpler for the following, 45678×9+5=45678×(10−1)+5

=456780−45678+5=411107 456789×9+6=456789×(10−1)+6

=4567890−456789+6=4111107

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