Question

The number of terms of the series needed for the sum of the series 50 + 45 + 40 + ……….. becomes zero: (a) 22 (b) 21 (c) 20 (d) None of these

Answer 1

21 terms

Sn=n/2(2a+n-1)d

0= n/2(2x50+(n-1)-5)

then n=21

Answer 2

Concept:

Arithmetic sequence is a series of number which consists of same difference between every term and next term.

If the first term of Arithmetic series is a and the common difference is d then the sum of n terms of that series is given by,

S = n/2 [2a+(n-1)d]

Given:

The given series is 50 + 45 + 40 + ................

Find:

We have to find the number of series of the above series whcih have the sum of zero.

Solution:

Given that, the series is 50, 45, 40, .............

Difference between every term and next term is,

45-50 = 40-45 = -5, which is constant

Hence it is a arithmetic sequence.

Let the sum of n terms of the given series is zero.

We have to find the value of n.

The sum of n terms is = n/2 [2*50+(n-1)(-5)] = n/2 [100-5n+5] = n/2 [105-5n]

According to condition,

n/2 [105-5n] = 0

n[105-5n] = 0

Either, n=0, it is not acceptable since number of terms cannot be zero.

Or,

105-5n = 0

5n = 105

n = 105/5 =21

The sum of 21 terms of that series is 0.

Hence the number of terms of the series needed for the sum of the series 50+45+40+ ...... becomes zero is (b) 21.

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