Question

1.
Discover the pattern in each and
extend it to three more places:
(i)1,4,9,16
(ii)3,10,17,24
(iii) 1,9, 17,24
(iv)2,13,24,35
Find the number of line segments,
, without actually counting them, for the number of points
7,8 and 9 marked on the same line.
Can a rectangular number also be a square number!
3.
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Answer 1

Answer:

(I)25,36,49

(II)31,38,45

(III)33,41,49

(IV)46,57,68

Step-by-step explanation:

(I)the general trend can be seen as: 4-1=3, 9-4=5, 16-9=7

hence the next number must be 16+9=25, 25+11=36 and 36+13=49

(II) here the general trend can be seen as a difference of 7 between each number. hence 24+7=31, 31+7=38, 38+7=45

(III) here every consecutive number is 8 more than the previous one

1+8=9, 9+8=17, 17+8=25 therefore next numbers are 25+8=33, 33+8=41 and 41+8=49

(IV) here every consecutive number is 11 more than the previous one

2+11=13, 13+11=24, 24+11=35 and so on

35+11=46, 46+11=57, 57+11=68

                                                 

Answer 2

2,13,24,35,more places:

(i)1,4,9,16

(ii)3,10,17,24

(iii) 1,9, 17,24

(iv)2,13,24,35