Mathematics
If the sum of first n terms of an A.P. is Sn = 5n2 + 3n, then its common difference is:
8
10
18
26
Answer
Given,
Sn = 5n2 + 3n
We know that,
nth term of A.P. :
∴ Tn = Sn - Sn - 1
= 5n2 + 3n - [5(n - 1)2 + 3(n - 1)]
= 5n2 + 3n - [5(n2 - 2n + 1) + 3n - 3]
= 5n2 + 3n - [5n2 - 10n + 5 + 3n - 3]
= 5n2 + 3n - 5n2 + 10n - 5 - 3n + 3
= 10n - 2
d = an - an - 1
= 10n - 2 - [10(n - 1) - 2]
= 10n - 2 - [10n - 10 - 2]
= 10n - 2 - 10n + 10 + 2
= 10.
Hence, option 2 is the correct option.
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0
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For what value of k will 2k + 1, 3k + 3, and 5k − 1 be three consecutive terms of an A.P.?
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The first and the last terms of an A.P. are 1 and 11 respectively. If the sum of its terms is 36, then the number of terms is :
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The sum of first 40 positive integers divisible by 6 is :
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