The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference. Hence find the sum of the series to 8 terms.
Let 'a' be the first term and 'd' be the common difference of given A.P.
Now,
4th term = 22
a + 3 d = 22 ............( i )
15th term = 66
a + 14 d = 66 ............( ii )
Subtracting ( i ) from ( ii ), we have
11 d = 44
d = 4
Substituting the value of 'd' in ( i ), we get
a = 22 - 3 x 4
= 22 - 12
= 10
First term = 10.
Now,
Use Graph paper for this question. A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded:
Height in cm | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 |
No. of boys | 4 | 8 | 20 | 14 | 7 | 6 | 1 |
Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other
axis draw an ogive of the above distribution. Use the graph to estimate the following:
(i) the median
(ii) lower Quartile
(iii) if above 158 cm is considered as the tall boys of the class. Find the number of
boys in the class who are tall.