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Find the sum of the first n terms of th...

Find the sum of the first n terms of the series :
`3 + 7 + 13 +21 + 31 +..........`

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To find the sum of the first \( n \) terms of the series \( 3 + 7 + 13 + 21 + 31 + \ldots \), we will follow these steps: ### Step 1: Identify the Pattern First, we need to identify the pattern in the series. Let's write down the terms: - \( a_1 = 3 \) - \( a_2 = 7 \) - \( a_3 = 13 \) - \( a_4 = 21 \) ...
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NCERT-SEQUENCES AND SERIES-MISCELLANEOUS EXERCISE
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  4. Find the 20^(t h)term of the series 2xx4+4xx6+6xx8+.....+nterms.

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  5. Find the sum of the following series up to n terms: (i) 5 + 55 + 555 +...

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  7. A fanner buys a used tractor for Rs 12000. He pays Rs 6000 cash and a...

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  9. Find the sum of the following series up to n terms : (1^3)/1+(1^3+2^2...

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  10. If S1,S2,S3are the sum of first n natural numbers, their squares and ...

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  11. A G.P. consists of an even number of terms. If the sum of all the ter...

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

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  13. If a, b, c, d are in G.P., prove that (a^n+b^n),(b^n+c^n),(c^n+a^n)ar...

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  14. Let S be the sum, P the product and R the sum of reciprocals of n term...

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  15. The p^(t h),q^(t h)and r^(t h)terms of an A.P. are a, b, c, respectiv...

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  16. The sum of the first four terms of an A.P. is 56. The sum of the last...

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  17. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0),then show that...

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  18. The sum of three numbers m GP is 56. If we subtract 1.7,21 from these...

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  19. If a\ a n d\ b are the roots of x^2-3x+p=0\ a n d\ c ,\ d are the root...

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  20. The ratio of the A.M. and G.M. of two positive numbers a and b, is m ...

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