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The nth term of a progression is 3^(n+1)...

The nth term of a progression is `3^(n+1)`. Show that it is a G.P. Also find its 5th term.

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729
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The nth term of a progression is 2^(n). Prove that it is G.P. Also find its common ratio.

(a) The sum of 'n' terms of a progression is n(n + 1). Prove that it is an A..P. Also find its 10th term. (b) The sum of 'n' terms of a progression is (3n^(2) - 5n). Prove that it is an A.P. (c) If the sum of n terms of a series is (5n^(2) + 3n) then find its first five terms.

If the nth term of a progression is (4n-10) show that it is an AP. Find its (i) first term, (ii) common difference, and (iii) 16th term.

The sum of n terms of a progression is (2^(n)-1) . Show that it is a GP and find its common ratio.

The sum of n terms of a series is n(n+1) . Prove that it is an A.P. also find its 10th term.

If the sum of the first n terms of a sequence is 2(7^(n)-1)//3 show that it is a G.P. Also , find its first term and common ratio.

The nth term of a sequence is given by a_(n)=2n+7 .Show that it is an A.P.Also,find its 7 th term.

(a) The nth term of a progression is (3n + 5) . Prove that this progression is an arithmetic progression. Also find its 6th term. (b) The nth term of a progression is (3 - 4n) . Prove that this progression is an arithmetic progression. Also find its common difference. (c) The nth term of a progression is (n^(2) - n + 1). Prove that it is not an A.P.

NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Exercise 9F
  1. The nth term of a progression is 3^(n+1). Show that it is a G.P. Also ...

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  2. Find the 7th term or'the G.P. 4 :- : s, 16, ... .

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  3. Find the 9th term of the G. P. 2, 1, (1)/(2),….

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  4. Find the 8th term of the G.P. sqrt(3),(1)/(sqrt(3)),(1)/(3sqrt(3)),......

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  5. Find the number of terms in the G.P. 1, 2, 4, 8, ... 4096.

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  6. Find the number of terms in the G.P. 1, - 3, 9, ... - 2187.

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  7. Find the 5th term from the end of the G .P. (1)/(512),(1)/(256),(1)/(1...

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  8. Find the, 4th terin from the end of the G .P. (5)/(2),(15)/(8),(45)/(3...

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  9. Which term of the progression sqrt(3),3,3sqrt(3)... is 729 ?

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  10. Which term of the progression 2, 8, 32,… is 131072 ?

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  11. If the nth terms of the progression 5, 10, 20, … and progression 1280,...

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  12. The 3rd, 7th and 11th terms of a G.P. are x, y and z respectively, the...

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  13. The 3rd and 6th terms of a G.P. are 40 and 320, then find the progress...

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  14. Find the G.P. whose 2nd and 5th terms are -(3)/(2)" and "(81)/(16) r...

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  15. if a G.P (p+q)th term = m and (p-q) th term = n , then find its p th t...

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  16. Find the G.P. whose 2nd term is 12 and 6th term is 27 times the 3rd te...

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  17. The first term of a G.P. is -3. If the 4th term of this G.P. is the sq...

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  18. The 4th, 7th and last terms of a G.P. are 10,80 and 2560 respectively....

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  19. Find the 4 terms in G .P. in which 3rd term is 9 more than the first t...

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  20. A manufacturer reckons that the value of a machine, which costs him...

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