Question

The sum of the first nterms of an A.p is given by sn=3n2-n.determine the a.p and its 25th term

Answer 1

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HOLA! USER

we know the formula =>

An = a + ( n-1 ) × d


SOLUTION :

Sn = 3n²- n (if we puts the value of n = 1)

=> Sn = 3(1)²-1

=> a1 = 3-1

=> a1 = 2

then, ( if we put the value of n = 2)

Sn = 3n²-n

=> a2 = 3(2)²-2

=> a2 = 3 × 4 - 2

=> a2 = 12 - 2

=> a2 = 10

then, we will find common difference so,

therefore, d = a2 - a1

=> d = 10 - 2 = 8

=> d = 8.

now, we will find the Ap of 25th term.

=> An = a + ( n - 1 ) × d


=> An = 2 + ( 25 - 1 ) × 8


=> An = 2 + 24 × 8


=> An = 2 + 192


=> An = 194

so, the Ap of 25th term is 194.


HoPe iTs HeLpFuL

Answer 2

Hey there !!

Given:-

→ S $\tiny n$ = 3n² - n.

To find:-

→ AP.

→ 25th term.

Solution:-

→ S $\tiny n$ = 3n² - n.

[taking n = 1 ]

→ S $\tiny 1$ = 3×1² - 1.

=> S $\tiny 1$ = 3 -1.

=> S $\tiny 1$  = 2.

⇒NOW, taking n = 2.

→S $\tiny 2$ = 3×2²-2.

→S $\tiny 2$ =12-2.

→S $\tiny 2$ =10.

⇒S $\tiny 1$ = a $\tiny 1$  .

So, a $\tiny 1$  =2.

And, a $\tiny 2$ =S $\tiny 2$ -S $\tiny 1$ .

⇒a $\tiny 2$ =10-2.

⇒a $\tiny 2$ =8.

So, d= a $\tiny 2$ - a $\tiny 1$ .

⇒d = 8 - 2 .

⇒d=6.

Hence, AP is 2 , 8 , 14 , ....... .

Now, 25th term is given by:-

= a + ( n -1 )d.

= 2 + ( 25 - 1 )6.

= 2 + 24 × 6.

= 2 + 144.

= 146.

Hence, it is solved.

THANKS

#BeBrainly.