Question

Question 1 Which term of the A.P. 121, 117, 113 … is its first negative term? [Hint: Find n for an < 0]

Class 10 - Math - Arithmetic Progressions Page 115

Answer 1

just find the ceil of number where term is zero

Answer 2

General term or nth term of A.P

The general term or nth term of A.P is given by an = a + (n – 1)d,
where a is the first term, d is the common difference and n is the number of term.
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Solution:

Given:first term(a)= 121 
common difference (d)= 117- 121 = -4
∵ n th term of an AP

an = a + (n – 1)d
⇒121+(n-1) ×(-4)
⇒121-4n+4
⇒12+4-4n
⇒125 -4n
an= 125 -4n

For first negative term , an <0
⇒ 125-4n<0
⇒125<4n
⇒4n>125
⇒n>125/4
⇒n> 31 1/4

least integral value of n= 32

Hence, 32nd term of the given AP is the first negative term. 

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Hope this will help you...