Find the sum of the series whose nth term is given by:
`(4n^(3)+6n^(2)+2n)`
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The sum of `25` terms of an `A.P.`, whose all the terms are natural numbers, lies between `1900` and `2000` and its `9^(th)` term is `55`. Then the fi
Correct Answer - C `(c )` Let the first term be `a` and the common difference `d`. Then it is given that `a+8d=55` and ……..`(i)` `1900 lt (25)/(2)(2a+24d) lt 2000` `:.1900...
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There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. T
Correct Answer - B `(b)` Sequence is `t_(1)+t_(2)+t_(3)+t_(4)+…` `t_(3)=t_(1)+t_(2)`, `t_(7)=1000` `t_(1)=1` but `t_(7)=t_(1)+t_(2)+t_(3)+t_(4)+t_(5)+t_(6)` `1000=2(t_(1)+t_(2)+t_(3)+t_(4)+t_(5))` `=4(t_(1)+t_(2)+t_(3)+t_(4))` `=8(t_(1)+t_(2)+t_(3))` `=16(t_(1)+t_(2))` `:.t_(1)+t_(2)=125//2` `:. t_(2)=125//2-1=123//2`
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9. Write notes on: (a) Continuous series (b) Discrete series (c) Individual series
(a) Continuous series is the third series followed by individual and discrete series. (b) In these series all the items are divided in certain groups, but these groups are not continuous, therefore...
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If the 8th term of an A.P. is 31 and the 15th term is 16 more than the 11th term, find the A.P.
Correct Answer - `3,7,11,15,19"……"`
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when the jaws of a standard vernier calipers are closed if the nth division of the veriner scale coincides with the nth M.S.D the zero error is `"____
Correct Answer - `+n xx L.C. `
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Find the sum of the series whose nth term is given by: `(3n^(2)+2n)`
Correct Answer - `(1)/(2)n(n+1)(2n+3)`
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Find the sum of `n` terms of the series whose `n t h` term is: `2n^2-3n+5`
Correct Answer - `(n)/(6)(4n^(2)-3n+23)`
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Find: (i) the 20th term of the AP 9, 13, 17, 21, … (ii) the 35 th term of the AP 20, 17, 14, 11,… (iii) the 18th term of the AP `sqrt(2), sqrt(18), sq
Correct Answer - (i) 85 (ii) -82 (iii) `35sqrt(2) (iv) 4(3)/(4)` (v) 310
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Determine the general term of an A.P. whose `7t h` term is `-1` and `16 t h` term 17.
Correct Answer - `T_(n) = (2n-15)`
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(i) The sum of the first n terms of an AP is `((5n^(2))/(2) + (3n)/(2))`. Find the nth term and the 20th term of this AP. (ii) The sum of the first n
Correct Answer - `(i) T_(n) = (5n-1), T_(20) = 99 (ii) T_(n) = (3n +1), T_(25) = 76`
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