Question

the sum of the first n terms of an AP is given by sn=3n2-n , determine the AP and its 25thterm.

Answer 1

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Answer 2

Answer:

A.p. = 2,8,14,....

25th term = 146                                

Step-by-step explanation:

Sum of first n terms = $S_n=3n^2-n$

Substitute n =1

So, $S_1=3(1)^2-1$

$S_1=2$

thus the first term of A.P. is 2

Substitute n = 2

$S_{2}=3(2)^2-2$

$S_{2}=10$

Thus sum of first two term is 10 i.e. $a_1+a_2=10$

So, $2+a_2=10$

$a_2=8$

So, second term of A.P. is 8

Common difference = $d = a_2-a_1 =8-2=6$

So, nth term of A.P. = $a_n=a+(n-1)d$

where a is the first term

d is the common difference

So, nth term of given A.P. is $a_n=2+(n-1)6$  --1

Now substitute n = 25 in 1

$a_{25}=2+(25-1)6$

$a_{25}=2+24 \times 6$

$a_{25}=146$

So, A.p. = 2,8,14,....

25th term = 146