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nth Term of an AP

The nth term ...

Question

The nth term of an A.P., the sum of whose n terms is S_n, is

(a) S_n + S_n−1

(b) S_n− S_n−1

(c) S_n + S_n+1

(d) S_n − S_n+1

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Solution

A.P. we use following formula,

So, the n^th term of the A.P. is given by . Therefore, the correct option is (b).

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Q. The common difference of an A.P., the sum of whose n terms is S_n, is

(a) S_n − 2S_n−1+ S_n−2

(b) S_n − 2S_n−1− S_n−2

(c) S_n − S_n−2

(d) S_n − S_n−1

S_{n}

denotes the sum of n terms of an A.P, then

S_{n + 3} - 3 S_{n + 2} + 3 S_{n + 1} - S_{n} =

s_{n}

denote the sum to

n

terms of an A.P., then

s_{n + 3} - 3 s_{n + 2} + 3 s_{n + 1} - s_{n}

Q. In an Arithmetic sequence,

S_{n}

represents the sum to

n

S_{n} - S_{n - 1}

?

S_{n}

, the sum of first

n

terms of an A.P., is given by

S_{n} = 5 n^{2} + 3 n

, then find its

n^{t h}

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