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The sum of first ten terms of an A.P. is...

The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. is 9. The first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to the common difference of the A.P. Find the two progressions.

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`(3+6+12+….),(2//3+25//3+625//6+....)`
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The sum oif the first ten terms of an A.P. is equal to 155, and the sum of the first two terms of a G.P. is 9. Find these progressionsif the first term of the A.P. equals the common ratio of the G.P. and the 1st term of G.P. equals the common difference of A.P.

The sum of the fist ten terms of an A.P. , equals 155 and the sum of the first two terms of a G.P. equals 9. The first term of the A.P. is equal to the common ratio of the G.P. and the common difference of the A.P. is equal to the first term G.P.. Give that the common difference of the A.P. is less then unity, which of the following is correct ?

If sum of first 20 terms of an A.P. is equal to sum of first 30 terms of the A.P. then sum of the first 50 terms of the A.P. is

If the sum of first 7 terms of an A.P. is 49 and that of its 17 terms is 289, find the sum of first n terms of the A.P.

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MOTION-SEQUENCE & SERIES -Exercise -3 Subjective /JEE Advanced
  1. The sum of infinite number of terms of a G.P. is 4 and the sum of thei...

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  2. Sum of the following series (i) 1+(2)/(2)+(3)/(2^2)+(4)/(2^3)+……..to...

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  3. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

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  4. In a set of four number, the first three are in GP & the last three ar...

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  5. Find the 4^(th) term of an H.P., whose 7^(th) term is 1/20 and 13^(th)...

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  6. Find the sum of the n terms of the series whose nth term is (i) n(n+...

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  7. Find the sum of the series (5)/(13)+(55)/(13)^2+(555)/(13)^2+(5555)/((...

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  8. If the expression exp {1+|cosx|+cos^(3)x|+cos^(4)x+ . . . . oo)log(e...

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  9. The sum of the infinite series , 1^2- 2^2 / 5+ 3^2 / 5^2 - 4^2 / 5^3 +...

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  10. Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...

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  11. Find the sum of the first n terms ofthe sequence : 1+2(1+1/n)+3(1+1/n)...

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  12. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

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  13. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  14. If a1,a,a3...an are in A.P then prove that a1^2-a2^2+a3^2-a4^2+....a(2...

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  15. If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...

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  16. Using the relation A.M ge G.M. Prove that (i) tan theta +cot theta g...

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  17. Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c), where a,b,c gt 0 .

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  18. The arithmetic mean of two numbers is 6 and their geometric mean G and...

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  19. In a circle of radius R a square is inscribed, then a circle is inscri...

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  20. 9. Find three numbers a,b,c between 2 & 18 such that; (G) their sum is...

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