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1,2,4,8,16,"…."...

`1,2,4,8,16,"…."`

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To solve the problem, we need to analyze the given sequence: `1, 2, 4, 8, 16, ...`. We will determine if this sequence is an arithmetic progression (AP), geometric progression (GP), or neither, and whether it is increasing or decreasing. ### Step-by-Step Solution: 1. **Identify the Terms of the Sequence:** - Let's denote the terms of the sequence as follows: - \( A_1 = 1 \) - \( A_2 = 2 \) ...
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Statement 1 1,2,4,8,"….." is a GP, 4,8,16,32,"…." is a GP and 1+4,2+8,4+16,8+32,"…." is also a GP. Statement 2 Let general term of a GP with common ratio r be T_(k+1) and general term of another GP with common ratio r be T'_(k+1) , then the series whode general term T''_(k+1)=T_(k+1)+T'_(k+1) is also a GP woth common ratio r.

Is 2,4,8,16"……." an arithmetic progression ?

The sequence 2,4,8,16,…..

Write the following sets in the set-builder form : (i) A = {2,4,6,8,10} (ii) B = {1,2,3,4,6,12} (iii) C= {1,3,5,7,9….} (iv) D={(1)/(2),(1)/(3),(1)/(4),...} (v) E={2,4,8,16,32,64} .

Which fraction comes next in the sequence : 1/2,3/4,5/8, 7/16, ?

Compute the following: [[-1,4,-6],[8,5,16],[2,8,5]]+[[12,7,6],[8,0,5],[3,2,4]]

Find the following sums -2+4-8+16-…..

If, A=[(1,1,2),(0,-3,5),(-2,3,4)] ,then is 4A=[(4,4,8),(0,-12,20),(-8,12,16)] ?

ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. 1,2,4,8,16,"…."

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  2. Let a, b, c be in A.P. and |a|lt1,|b|lt1|c|lt1. If x=1+a+a^(2)+ . . . ...

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  3. If an=3/4-(3/4)^2+(3/4)^3+...(-1)^(n-1)(3/4)^n and bn=1-an, then find ...

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  4. If a1, a2, a3, be terms of an A.P. if (a1+a2++ap)/(a1+a2++aq)=(p^2)/(...

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  5. If a1, a2, a3,.....an are in H.P. and a1 a2+a2 a3+a3 a4+.......a(n-1...

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  6. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  7. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  8. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  9. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  10. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  11. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  12. in a geometric progression consisting of positive terms, each term eq...

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  13. Suppose four distinct positive numbers a(1),a(2),a(3),a(4) are in G.P....

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  14. The first two terms of a geometric progression add up to 12. The su...

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  15. If the sum of first n terms of an AP is cn^(2), then the sum of square...

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  16. 1+2/3+6/(3^2)+10/(3^3)+14/(3^4)+...oo=

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  17. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

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  18. Le a1, a2, a3, ,a(11) be real numbers satisfying a2=15 , 27-2a2>0a n ...

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  19. A person is to cout 4500 currency notes. Let a(n) denotes the number o...

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  20. The minimum value of the sum of real numbers a^(-5),a^(-4),3a^(-3),1,a...

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  21. A man saves Rs. 200 in each of the first three months of his service. ...

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