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Justify whether it is true to say that `-1, -3/2, -2, 5/2, …..from an AP as `a_2-a_1 = a_3-a_2`.

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Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequencea_1,a_2....a_n form and AP. Then a_1^1-a_2^2+a_3^2-a_4^2... is equal to

Three distinct numbers a_1 , a_2, a_3 are in increasing G.P. a_1^2 + a_2^2 + a_3^2 = 364 and a_1 + a_2 + a_3 = 26 then the value of a_10 if a_n is the n^(th) term of the given G.P. is:

If (b_2-b_1)(b_3-b-1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_2+a_3)/(2),(b_2+b_3)/(2)) .

AGRAWAL PUBLICATION-ARITHMETIC PROGRESSIONS-EXAMPLE
  1. Find the number of terms in the A.P: 18, 15 1/2,13,…., -47.

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  2. Find the common difference of the Arithmetic Progression (A.P)

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  3. Justify whether it is true to say that -1, -3/2, -2, 5/2, …..from an A...

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  4. How many 2-digit numbers are divisuble by 3?

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  5. In an AP, if the common difference (d) = -4, and the seventh term (a7)...

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  6. Write the n^(th) term of the A.P. 1/m ,(1+m)/m, (1+2m)/m.

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  7. If the n^(th) term of the A.P. -1,4,9,14, … is 129, find the value of ...

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  8. Find the 9th term from the end (towards the first term) of the A.P. 5,...

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  9. For the AP: -3,-7,-11, ……, can we directly find a(30) - a(20) without ...

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  10. If the first three terms of an A.P are b, c abd 2b, then find the rati...

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  11. What is the common difference of an A,P in which a(21) - a7 =84?

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  12. For what value of k will k+9, 2k -1 and 2k+7 are the consecutive terms...

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  13. Find the 16^(th)term of the AP,2,7,12,17,……

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  14. Find the mean of first eleven natural numbers.

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  15. Show that (a+b)^2, (a^2 + b^2) and (a+b)^2 are in AP.

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  16. If the 17^(th) term of an A.P exceeds its 10^(th) term by 7, Find the ...

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  17. Hoe many multiples of 4 die between 10 and 205?

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  18. Determine the A.P. whose third term is 16 and 7^(th) term exceeds the ...

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  19. Two AP's have the same common difference.The first term of one AP is 2...

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  20. Which term of the AP 3,15,27, 39,…. Will be 120 more than its 21st ter...

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