Question

Question 2 Choose the correct choice in the following and justify
I. 30 th term of the A.P: 10, 7, 4, …, is
A. 97 B. 77 C. − 77 D. − 87
II 11 th term of the A.P. -3,-1/2, 2,... is
A. 28 B. 22 C. − 38 D. -48.1/2

Class 10 - Math - Arithmetic Progressions Page 106

Answer 1

AP  ( Arithmetic progression). 
 
A list of numbers a1 ,a2, a3  ………….. an is called an arithmetic progression , Is there exists a constant number ‘d’


a2= a1+d
a3= a2+d
a4= a3+d……..
an= an-1+d ………


Each of the numbers in the list is called a term .

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

This fixed  number is called the common difference( d ) of the AP.

General form of an AP.:
a, a+d, a+2d, a+3d…….

Here a is the first term and d is common difference.

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(i) 

Given that
A.P. 10, 7, 4, …

First term, a = 10
Common difference, d = a2 − a1 = 7 − 10 = −3

We know that, an = a + (n − 1) d

a30 = 10 + (30 − 1) (−3)
a30 = 10 + (29) (−3)
a30 = 10 − 87 = −77
Hence, the correct answer is option C.

(ii) 

Given that A.P. is -3, -1/2, ,2 …

First term a = – 3
Common difference, d = a2 − a1 = (-1/2) – (-3)
= (-1/2) + 3 = 5/2

We know that, an = a + (n − 1) d

a11 = 3 + (11 -1)(5/2)
a11 = 3 + (10)(5/2)
a11 = -3 + 25
a11 = 22
Hence, the answer is option B.

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Hope this will help you...

Answer 2

(i) Given that
A.P. 10, 7, 4, …
First term, a = 10
Common difference, d = a2 − a1 = 7 − 10 = −3
We know that, an = a + (n − 1) d
a30 = 10 + (30 − 1) (−3)
a30 = 10 + (29) (−3)
a30 = 10 − 87 = −77
Hence, the correct answer is option C.

(ii) Given that A.P. is -3, -1/2, ,2 ...
First term a = - 3
Common difference, d = a2 − a1 = (-1/2) - (-3)
= (-1/2) + 3 = 5/2
We know that, an = a + (n − 1) d
a11 = 3 + (11 -1)(5/2)
a11 = 3 + (10)(5/2)
a11 = -3 + 25
a11 = 22