Class X Session 2023-24 Question 5

                                                    

MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

Question 5

Two APs have the same common difference. The first term of one of these is –1 and that of 

the other is – 8. The difference between their 4th terms is:

(a)  1

(b) -7

(c)  7

(d)  9

Explanation : 

Since both arithmetic progressions (APs) have the same common difference, we can find the difference between their 4th terms by simply subtracting the corresponding first terms of the two progressions.

𝑎𝑛 = 𝑎1 + ( 𝑛 − 1 )𝑑 

where 𝑎𝑛 is nth term a1 is the first term,𝑛 is the term number, and d is the common difference. 

Given: First term of the first AP (𝑎1 ) = -1

First term of the second AP (𝑎2 ) = -8

The 4th term of an arithmetic progression is given by: 𝑎𝑛 = 𝑎1 + ( 𝑛 − 1 )𝑑  where 𝑎𝑛 is the 𝑛th term, 𝑎1 is the first term,n is the n term number, 

and d is the common difference.

For the first AP:𝑎4 = −1+(4−1)𝑑 = −1+3𝑑 ----------(1)

For the second AP: 𝑎4 =  −8 +(4−1)𝑑 = −8+3𝑑 -----(2)

According to the question, the difference between their 4th terms with help of  eq (1) and (2) 

Difference= (−1+3d) − (−8+3d) = ∣7∣ = 7

Guess the Option and comment below  👇