What is the sum of 11 terms of an arithmetic progression if the 4

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102.

The average of the first nine integral multiples of 3 is

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103.

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104.

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105.

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106.

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  • fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction


107.

The average weight of 15 oarsmen in a boat is increased by 1.6 kg when one of the crew who weighs 42 kg is replaced by a new man. Find the weight of the new man (in kg).

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108.

The average of 17 results is 60. If the average of first 9 results is 57 and that of the last 9 results is 65, then what will be the value of 9th result?

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109.

A batsman makes a score of 111 runs in the 10th match and thus increases his average runs per match by 5. What will be his average after the 10th match?

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110.

What is the sum of 11 terms of an arithmetic progression if the 4th term is 11 and the 7th term is -4?

  • -75

  • 55

  • 11

  • 100


C.

11

tn= a + (n -1)d
11 = a + (4 - 1)d
11 = a + 3d               ...(i)

tn =  a + (n - 1)d
-4 = a + (7 - 1)d
-4 = a + 6d               ...(ii)

Solving (i) and (ii), we get
a = 26,  d = -5

Now,
    straight S subscript straight n space equals space straight n over 2 left square bracket 2 straight a space plus space left parenthesis straight n space minus space 1 right parenthesis straight d right square bracket
straight S subscript 11 space equals space 11 over 2 open square brackets 2 space cross times space 26 space plus space left parenthesis 11 minus 1 right parenthesis space right parenthesis left parenthesis negative 5 right parenthesis close square brackets
straight S subscript 11 space equals space 11 over 2 open square brackets 52 space minus space 50 close square brackets space equals space 11 over 2 space cross times space 2
straight S subscript 11 space equals space 11


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