Question

Consider the following number pattern

3

10, 17

24, 31,38

..............................................

....................................................

a) Write next two lines of this sequence?

b) What is the sum of first 20 natural numbers?

c) What is the last term of 20 th line of this sequence?

d) Find the sum of all term​

Answer 1

Answer:

The first terms of each line are 4,7,13,22…

The difference between each consecutive term is

7-4 = 3

13-7 = 6

22-13 = 9

i.e. 3,6,9… in AP

For 4th line,

First term = 22 + 12 = 34 , d = 3

For 5th line

First term = 34 + 15 = 49 , d = 3

Also from observation, nth line has n terms

Hence, 4th line

34,37,40,43

And 5th line

49,52,55,58,61

The sequence of common difference is

The difference between the first terms of each line forms an AP which is

3,6,9…

For first term of 20th line, sum of 19 terms of above sequence to be added to first term of first line.

Sum of 19 terms =

= 570

For 20th line,

First term = 4 + 570 = 574

It has 20 terms

Last term = 574 + 19×3 = 574 + 57 = 631

Answer 2

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