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Sequence and Series

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Question : 38 of 86

Marks: +1, -0

If Sn be the sum of n terms of an A.P.; the value of

S_{n}-2 S_{n-1}+S_{n-2}

is

${d}$
${d}^{2}$
cannot calculated
None

Solution:

Concept:

Use the relationship between sum and terms:

S_n - S_{n-1} = T_n

(nth term).

Explanation:

S_n - 2S_{n-1} + S_{n-2} = (S_n - S_{n-1}) - (S_{n-1} - S_{n-2})

.

S_n - S_{n-1} = T_n

, the nth term, and

S_{n-1} - S_{n-2} = T_{n-1}

, the (n-1)th term.

Thus, the expression equals

T_n - T_{n-1} = d

, the common difference.

Answer:

The value is

d

.

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