Q1 of 50 Page 10

Look at these triangles with dots. How many dots are there in each?


Compute the number of dots needed to make the next two triangles.

The number of dots in first 3 triangles are 3, 6 and 10 respectively.

The difference between the first two terms is 6-3 = 3


And 10-6 = 4


The series continues 3, 4, 5…


Hence, this forms an AP with first term as 3 and common difference as 1


Next two terms are 4 + 1 = 5


And 5 + 1 = 6


So 4th pattern has 10 + 5 = 15 dots


5th pattern has 15 + 6 = 21 dots


More from this chapter

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2

Make the following number sequences from the sequence of equilateral triangles, squares, regular pentagons and so on, of regular polygons.

Number of sides – 3,4,5…


Sum of interior angles –


Sum of exterior angles –


One interior angle –


One exterior angle –

 3

Write down the sequence of natural numbers leaving remainder 1 on division by 3 and the sequence of natural numbers leaving remainder 2 on division by 3.

 4

Write down the sequence of natural numbers ending in 1 or 6 and describe it in two other ways.

 5

One cubic centimeter of iron weight 7.8 grams. Write as sequences, the volumes of weights of iron cubes of sides 1 centimetre, 2 centimetres and so on.