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Arithmetic Progressions Ex-5.4 Questions Answers

Subjects

Question 1 : Which term of the AP: 121, 117, 113, . . ., isits first negative term? [Hint: Find n for an < 0]

Answer 1 :

Given the AP series is 121, 117, 113, . . .,

Thus, first term, a = 121

Common difference, d = 117-121= -4

By the nth term formula,

an = a+(n −1)d

Therefore,

an = 121+(n−1)(-4)

= 121-4n+4

=125-4n

To find the first negative term of theseries, a< 0

Therefore,

125-4n < 0

125 < 4n

n>125/4

n>31.25

Therefore, the first negative term of the series is 32nd term.

Question 2 : The sum of the third term and the seventh term of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP?

Answer 2 :

Question 3 : A ladder has rungs 25 cm apart. (see Fig.5.7). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cmat the top. If the top and the bottom rungs are apart, what is the length of the woodrequired for the rungs? 

Answer 3 :

Solution

Question 4 : The houses of a row are numbered consecutivelyfrom 1 to 49. Show that there is a value of x such that the sum of the numbersof the houses preceding the house numbered x is equal to the sum of the numbersof the houses following it. Find this value of x. 

Answer 4 :