If the sequence <<an>> is A.P., show tha...

If the sequence `<>` is A.P., show that `a_(m+n)+a_(m-n)=2a_mdot\ `

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If a_(m) be the mth term of an AP, show that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+"...."+a_(2n-1)^(2)-a_(2n)^(2)=(n)/((2n-1))(a_(1)^(2)-a_(2n)^(2)) .

Find the indicated terms in each of the following sequences whose nth terms are: a_(n)=5_(n)-4;a_(12) and a_(15)a_(n)=(3n-2)/(4n+5);a+7 and a_(8)a_(n)=n(n-1);a_(5)anda_(8)a_(n)=(n-1)(2-n)3+n);a_(1),a_(2),a_(3)a_(n)=(-1)^(n)n;a_(3),a_(5),a_(8)

If a_(1), a_(2), a_(3),........, a_(n) ,... are in A.P. such that a_(4) - a_(7) + a_(10) = m , then the sum of first 13 terms of this A.P., is:

Find the indicated terms in each of the following sequences whose n^(th) terms are a_(n) = (a_(n-1))/(n^(2)) , (n ge 2) , a_(1) =3 , a_(2) , a_(3)

Is the sequence defined by a_(n) = 3n^(2) + 2 an A.P. ?

The nth term of a sequence is given by a_(n)=2n^(2)+n+1. Show that it is not an A.P.

The Fibonacci sequence is defined by 1=a_(1)=a_(2) and a_(n)=a_(n-1)+a_(n-2),n>2 Find (a_(n+1))/(a_(n)),f or n=5

The fibonacct sequence is defined by 1=a_(1) = a_(2) and a_(n-1) + a_( n-1) , n gt 1 Find (a_(n+1))/(a_(n)) " for " n =1 ,2,34,5,

If a_(1),a_(2),a_(3)............ are in A.P. such that a_(4)-a_(7),+a_(10)=m, then sum of 13 terms of this A.P., is;

VK GLOBAL PUBLICATION-ARITHMETIC PROGRESSIONS -PROFICIENCY EXERCISE ( SHORT ANSWER QUESTION I)

The general term of a sequence is given by an=-4n+15 . Is the se...
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Write the sequence with nth terms: an=3+4n (ii) an=5+2n an=6-n (iv) a...
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Find the 6t h term from the end of the AdotPdot 17 ,\ 14 ,\ 11 ,\ d...
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Which term of the A.P. 21 ,\ 42 ,\ 63 ,\ 84 ,\ dot is 420?
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Which term of the AP: 115, 110, 105,.............is its first negative...
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If the sum of the first q terms of an AP is 2q + 3q^(2), what is its c...
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Find the common difference of an AP whose first term is 4, the last te...
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How many terms are there in the A.P. -1,\ -5/6,\ -2/3,-1/2,\ ,(10)/3?
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In an A.P., the sum of first n terms is (3n^2)/2+(13)/2n . Find its...
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If the sequence <<an>> is A.P., show that a(m+n)+a(m-n)=2amdot\
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Which of the following form an ap ? Justify your answer 0, 0, 1, 1, ...
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Which of the following form of an AP ? Justify Your answer. (i) -1,-...
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Which of the following form an ap ? Justify your answer sqrt(3),sqrt...
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Is 0 a term of the AP 31, 28, 25, …? Justify your answer.
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Is the sum of m terms of an AP always less than the sum of (m +1) term...
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Is it true to say that an=3n^(2) + 5 is the n^(th) term of an A.P. seq...
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For the AP -3, -7, -11, … can we find directly a(30)-a(20) without ac...
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The first and the last terms of an AP are 7 and 49 respectively. If...
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The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term ...
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The sum of the first n terms of an A.P. is 4n^2+2n . Find the n ...
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