Find the sum of `n` terms of the series whose `n t h` term is: `2n^2-3n+5`
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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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If the sum of the first `100` terms of an `AP` is `-1` and the sum of even terms lying in first `100` terms is `1`, then which of the following is not
Correct Answer - D `(d)` `x_(1)+x_(2)+x_(3)+……+x_(100)=(100)/(2)(x_(1)+x_(100))=-1` `impliesx_(1)+x_(100)=-(1)/(50)` `x_(2)+x_(4)+…+x_(100)=(50)/(2)(x_(1)+d+x_(100))=1` `impliesx_(1)+x_(100)+d=(1)/(25)` `impliesd=(3)/(50)` ltbr `x_(1)+x_(1)+99d=(-1)/(50)` `impliesx_(1)=(-149)/(50)` `x_(100)=x_(1)+99d` `=(-149)/(50)+99xx(3)/(50)` `=(74)/(25)`
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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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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 the series whose nth term is given by: `(4n^(3)+6n^(2)+2n)`
Correct Answer - `n(n+1)^(2)(n+2)`
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Find the sum to `n` terms of the series: `1+5+12+22+35+`
Correct Answer - `(1)/(2)n^(2)(n+1)`
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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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Find the sum of each of the following Aps: (i) 2, 7, 12, 17, … to 19 terms (ii) 9, 7, 5, 3,…. To 14 terms. (iii) -37, -33, -29,… to 12 terms (iv) `(1)
Correct Answer - (i) 893 (ii) -56 (iii) - 80 (iv) `(33)/(20)` (v) 5505
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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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An AP 5, 8, 11…has 40 terms. Find the last term. Also find the sum of the last 10 terms.
First Term of the AP (a) = 5 Common difference (d) = 8 - 5 = 3 Last term = a40 = a + (40 - 1) d = 5 + 39 × 3...
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