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A sequence is called an A.P if the diff...

A sequence is called an A.P if the difference of a term and the previous term is always same i.e if `a_(n+1)- a_(n)= ` constant ( common difference ) for all `n in N `
For an A.P whose first term is 'a ' and common difference is d is
`S_(n) = n/2 (2a +(n-1)d)=n/2 (a+a+(n-1)d)= n/2 (a+l)`

1. A sequence whose `n^(th)` term is given by `t_(n) = An + N ` , where A,B are constants , is an A.P with common difference
A. 2
B. 1
C. A
D. B

If sum of n terms `S_n` for a sequence is given by `S_n=An^2+Bn+C`, then sequence is an A.P. whose common difference is
A. A
B. B
C. 2A
D. 2B

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Knowledge Check

  • For an A.P. if the first term is 8 and the common difference is 8, then S_(n) =

    A
    `2n(n-1)`
    B
    `4n(n-1)`
    C
    `2n(n-1)`
    D
    `4n(n+1)`

  • Sum of first n terms of an A.P. whose last term is l and common difference is d, is

    A
    `(n)/(2) [ l + (n-1)d]`
    B
    `(n)/(2) [ l-(n-1)d]`
    C
    `(n)/(2) [2l + (n-1) d]`
    D
    `(n)/(2) [2l-(n-1)d]`

  • A sequence is called an A.P if the difference of a term and the previous term is always same i.e if a_(n+1)- a_(n)= constant ( common difference ) for all n in N For an A.P whose first term is 'a ' and common difference is d has n^(th) term as t_n=a+(n-1)d Sum of n terms of an A.P. whose first term is a, last term is l and common difference is d is S_(n) = n/2 (2a +(n-1)d)=n/2 (a+a+(n-1)d)= n/2 (a+l) If sum of n terms S_n for a sequence is given by S_n=An^2+Bn+C , then sequence is an A.P. whose common difference is

    A
    A
    B
    B
    C
    2A
    D
    2B

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    Show that the sequence defined by a_(n) = m + (2n - 1) d, where m and d are constants , is an A.P. Find its common difference .

    A sequence is called an A.P if the difference of a term and the previous term is always same i.e if a_(n+1)- a_(n)= constant ( common difference ) for all n in N For an A.P whose first term is 'a ' and common difference is d has n^(th) term as t_n=a+(n-1)d Sum of n terms of an A.P. whose first term is a, last term is l and common difference is d is S_(n) = n/2 (2a +(n-1)d)=n/2 (a+a+(n-1)d)= n/2 (a+l) a_1,a_2,a_3,....a_8 is an A.P. with common difference d. Then a_(8-2k)-a_k(1 leklt4 k in N) is equal to

    A sequence is called an A.P. if the difference of a term and the previous term is always same i.e. if a_(n+1)-a_(n) = constant (common difference) for all n in N . For an A.P. whose first term is 'a' and common difference is 'd' has its n^("th") term as t_(n)=a+(n-1)d Sum of n terms of an A.P. whose first is a, last term is I and common difference is d is S_(n)=(n)/(2)(2a+(n-1)d) =(n)/(2)(a+a+(n-1)d)=(n)/(2)(a+l) . S_(r) denotes the sum of first r terms of a G.P., then S_(n),S_(2n)-S_(n),S_(3n)-S_(2n) are in

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