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The first term of a G.P. is 1. The sum o...

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

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To solve the problem step by step, we will follow these steps: ### Step 1: Identify the terms of the G.P. The first term of the G.P. is given as \( a = 1 \). The common ratio is denoted as \( r \). ### Step 2: Write the expressions for the third and fifth terms The third term of the G.P. can be expressed as: \[ ...
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NCERT-SEQUENCES AND SERIES-MISCELLANEOUS EXERCISE
  1. Show that (1xx2^2+2xx3^2+......+nxx(n+1)^2)/(1^2xx2+2^2xx3+......+n^2x...

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

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

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

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  5. 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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  6. 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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  7. Let S be the sum, P the product and R the sum of reciprocals of n term...

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

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

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

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  14. Show that the sum of (m+n)^(t h)and (m-n)^(t h)terms of an A.P. is eq...

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  15. Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively...

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  16. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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  17. Find the sum of all numbers between 200 and 400 which are divisible b...

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  18. If f is a function satisfying f(x+y)=f(x)f(y)for all x ,y in Xsuch t...

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  19. Find the sum of all two digit numbers which when divided by 4, yields...

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  20. The first term of a G.P. is 1. The sum of the third term and fifth te...

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