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Common Difference

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How to prove the sum of first n term of an arithmetic progression

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Q. The sum of the first n terms of the arithmetic progression is equal to half the sum of the next n terms of the same progression. Find the ratio of the sum of the first 3n terms of the progression to the sum of its first n terms.

Q. The sum of first

^{'} n^{'}

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" 5 n^{2} - 2 n "

20^{t h}

Q. The sum of the first

n

terms of the sequence

a_{n}

is defined by the formula

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

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Q. If an arithmetic progression sum of first n terms is

{2 n}^{2} + 3 n

.Its common difference is:

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