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Show that for the sequence defined by ` a_(n) = (n -1) (n-2) ` ,the first two terms are zero and its fifth term is 12 .

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To solve the problem, we need to show two things about the sequence defined by \( a_n = (n - 1)(n - 2) \): 1. The first two terms are zero. 2. The fifth term is 12. Let's go through the steps: ### Step 1: Calculate the first term \( a_1 \) ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
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  6. Is the sequence defined by a(n) = 3n^(2) + 2 an A.P. ?

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  7. Show that the sequence (p + q)^(2), (p^(2) + q^(2)), (p-q)^(2) … is a...

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  8. Determine the number of terms in the A.P. 3,4,5, …, 399 . Also find ...

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  9. Find the indiated terms in each of the following A.P. (i) 1, 7, 1...

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  10. The 11^(th) of an A.P. is 80 and the 16^(th) term is 110 . Find the...

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  11. In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...

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  12. The sum of three numbers in A.P. is 27 and the sum of their squares i...

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  13. 4. (a) Divide 20 into 4 parts which are in A.P. and such that the prod...

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  14. about to only mathematics

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  15. If a ,b ,c are in A.P., prove that the following are also in A.P. (i) ...

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  16. If a^(2), b^(2),c^(2) are in A.P prove that (a)/(b+c), (b)/(c+a) ,(c)...

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  17. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P. prove that 1/(b-c),1/(c-a),1/(a...

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  18. If a,b,c are in A.P. prove that: a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are ...

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  19. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

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  20. Find the sum of all integers from 1to 1001.

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