Question

Plz Help!!!! Find the first term, the common difference, and tn for a series having Sn = 5n^2−n.

Answer 1

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Answer 2

The first term is 4.

The common difference is 10.

The nth term is $T_n=10n-6$

Step-by-step explanation:

Given : A series having $S_n = 5n^2-n$

To find : The first term, the common difference, and tn for a series ?

Solution :

$S_n = 5n^2-n$

Put n=1,

$S_1= 5(1)^2-1=4$

The first term is 4.

Put n=2,

$S_2= 5(2)^2-2=18$

$a_1+a_2= 18$

$4+a_2=18$

$a_2=18-4$

$a_2=14$

The common difference is $d=a_2-a_1$

$d=14-4$

$d=10$

The common difference is 10.

The nth term of a series is $T_n=a+(n-1)d$

$T_n=4+(n-1)10$

$T_n=4+10n-10$

$T_n=10n-6$

The nth term is $T_n=10n-6$

#Learn more

Find the first term, the common difference, and tn for a series having Sn = 3n^5+5n.

t1=, d= , tn=

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