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Find the indicated terms in each of the ...

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)`

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AI Generated Solution

To find the indicated terms \( a_2 \) and \( a_3 \) in the sequence defined by the recurrence relation \( a_n = \frac{a_{n-1}}{n^2} \) for \( n \geq 2 \) and the initial term \( a_1 = 3 \), we will follow these steps: ### Step 1: Calculate \( a_2 \) Using the formula for \( n = 2 \): \[ a_2 = \frac{a_{1}}{2^2} \] ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
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  2. Find the indicated terms in each of the following sequences whose n^(...

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  3. Find the indicated terms in each of the following sequences whose n^(...

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  4. Find the first five terms of the sequence whose general term is given ...

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  5. Find the first five terms of the sequence whose general term is given ...

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  7. Show that for the sequence defined by a(n) = (n -1) (n-2) ,the first...

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  8. Find the first five terms of the following sequences and write down th...

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  9. Write the first five terms of the following sequences and obtain the ...

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

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

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

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

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

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

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

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

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  18. about to only mathematics

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

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

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