Home
Class 10
MATHS
Difference of mth and nth term of an A.P...

Difference of mth and nth term of an A.P. =(m-n)d.

Text Solution

AI Generated Solution

The correct Answer is:
To determine whether the statement "Difference of mth and nth term of an A.P. = (m-n)d" is true or false, we will derive the difference step by step. ### Step-by-Step Solution: 1. **Define the terms of the A.P.** Let the first term of the A.P. be \( a \) and the common difference be \( d \). 2. **Write the formula for the mth term.** The mth term of the A.P. can be expressed as: \[ a_m = a + (m-1)d \] 3. **Write the formula for the nth term.** The nth term of the A.P. can be expressed as: \[ a_n = a + (n-1)d \] 4. **Calculate the difference between the mth and nth terms.** We need to find the difference \( a_m - a_n \): \[ a_m - a_n = \left( a + (m-1)d \right) - \left( a + (n-1)d \right) \] 5. **Simplify the expression.** When we simplify the above expression, the \( a \) terms cancel out: \[ a_m - a_n = (m-1)d - (n-1)d \] This can be further simplified to: \[ a_m - a_n = (m-1 - (n-1))d = (m - n)d \] 6. **Conclusion.** Thus, we find that the difference between the mth and nth terms of an A.P. is: \[ a_m - a_n = (m - n)d \] This confirms that the statement "Difference of mth and nth term of an A.P. = (m-n)d" is **true**.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION

    CBSE COMPLEMENTARY MATERIAL|Exercise SHORT ANSWER TYPE QUESTIONS-I|19 Videos

  • ARITHMETIC PROGRESSION

    CBSE COMPLEMENTARY MATERIAL|Exercise SHORT ANSWER TYPE QUESTIONS-II|17 Videos

  • ARITHMETIC PROGRESSION

    CBSE COMPLEMENTARY MATERIAL|Exercise MATCH THE FOLLOWING:|1 Videos

  • AREAS RELATED TO CIRCLES

    CBSE COMPLEMENTARY MATERIAL|Exercise PRACTICE-TEST ( AREAS RELATED TO CIRCLES ) SECTION-D|1 Videos

  • CIRCLES

    CBSE COMPLEMENTARY MATERIAL|Exercise PRACTICE - TEST (SECTION - D)|1 Videos

Similar Questions

Explore conceptually related problems

If the A.M. between mth and nth terms of an A.P. be equal to the A.M. between pth and qth terms of an A.P. then prove that m+n=p+q .

The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2) . Show that the ratio mth and nth term is (2n-1) : (2n-1).

Knowledge Check

  • If m times the mth term of an AP with non-zero common difference equals n times the nth term of an AP, where m ne n , then (m+n)th term of this AP is

    A
    mn
    B
    zero
    C
    2mn
    D
    None

  • If m times the mth term of an A.P. with non-zero common difference equals n times the nth term of the A.P., where m ne n , then (m+n)th term of this A.P. is

    A
    (m+n) times mth term
    B
    zero
    C
    m+n
    D
    `-(m+n)`

    • Similar Questions

    Explore conceptually related problems

    Question on nth terms in A.P.

    The ratio of the sums of m terms and n terms of an A.P. is m^(2) : n^(2). Prove that the ratio of their mth and nth term will be (2m - 1) : (2n-1).

    For an AP, it is given that first term (a)= 5 and Common Difference (d) = 3 and nth term = 50. Find n and sum of first n terms of AP

    If m^(th) n^(th) and o^(th) term of an A.P. are n, o and m. Find common difference d.

    The sum of the first n terms of an A.P.is 4n^(2)+2n. Find the nth term of this A.P.

    (iv) Show that the sum of (m+n)^(t)h and (m-n)^(th) term of an AP is equal to twice the mth term?

    Home
    Profile