if the sum to n terms of a sequence be [tex]n2 + 2n[/tex] then prove that the sequence is an ap
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sanjushelar
Write any 5 expression which are polynomial
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Arceus11 Is the sum of n terms of a sequence. So substitute n=1 in the formula given to the answer as 3 for the sum of 1 term I.e the first term of the sequence is 3. Now substitute n=2 in the formula to get the sum of first two terms as 8. Let denote the sum of two terms. Thus Now subtract S2-S1 =8-3=5. This is the second term in the sequence. Doing this likewise, you get 7 as the third term, and 9 as the fourth term and so on. This the difference between the consecutive terms turns out to be constant, proving that it is and A.P with common difference as 2.
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Is the sum of n terms of a sequence. So substitute n=1 in the formula given to the answer as 3 for the sum of 1 term I.e the first term of the sequence is 3.
Now substitute n=2 in the formula to get the sum of first two terms as 8. Let denote the sum of two terms. Thus
Now subtract S2-S1 =8-3=5.
This is the second term in the sequence. Doing this likewise, you get 7 as the third term, and 9 as the fourth term and so on.
This the difference between the consecutive terms turns out to be constant, proving that it is and A.P with common difference as 2.