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Find the first term, the common difference and t_n for a series having S_n=3n^2+5n

Find the first term, the common difference and t_n for a series having S_n=3n^2+5n-example-1
User DeeBo
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1 Answer

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Given that

Sn=3n^2+5n​

t1 = S1

=3(1^2) + 5(1)

= 3 + 5

= 8

The sum of the first 2 terms

= 3(2^2) + 5(2)

= 12 + 10

= 22

If the first term is 8 then the second

= 22 - 8

= 14

Ther common difference which is the difference between the second and the first

= 14 - 8

= 6

tn = 8 + (n - 1)6

= 8 + 6n - 6

= 8 - 6 + 6n

= 6n + 2

Hence, the first term is 8, the common difference is 6 and the nth term tn is 6n + 2

User Becca Petrin
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