Question

The first term of an AP is 5 and the sum of the first 12 terms is 258. Find the 12th term. ​

Answer 1

Answer:

If the first term of an AP is 5 and the sum of first 12 terms is 258, then the 12 th term is 38

Step-by-step explanation:

Given

First term of the AP = 5

Sum of the first 12 terms = 258

The sum of n terms in an AP is given by equation

$S_{n}= \frac{n}{2} (a+a_{n} )$

Where

$S_{n}$ is sum of n terms,

a is the first term

And $a_{n}$ is the nth term

We have to find the 12 th term that is $a_{12}$

Here, given

n=12

$S_{12}$ =258

a= 5

Substituting, we get

$258=\frac{12}{2} (5+a_{12})$

$258=6(5+a_{12})\\258=30+6a_{12}$

$6a_{12}=258-30\\ a_{12}=\frac{228}{6} \\ \\ = 38$

So the 12 th term of AP is 38



Answer 2

Given: The first term of an A.P. (a)=5

           Number of terms(n)=12

       The sum of the first 12 terms(S12)=258

To find The 12th term.

Solution: The series of numbers is said to be in Arithmetic Progression or A.P. if the numbers possess a constant difference.

We know that

Sum of the nth term of an A.P.(Sn)=n/2{2a+(n-1)d} [where d=common difference]

⇒S12=12/2{(2×5)+(12-1)d}    [∵ a=5,n=12 from above]

⇒258=6×{10+11d}

⇒258=60+66d

⇒258-60=66d

⇒66d=258-60

⇒66d=198

⇒d=198/66

⇒d=3

We know that The nth term(an)=a+(n-1)d

⇒a12=5+(12-1)×3  [∵ we calculate the value of d above]

⇒a12=5+(11×3)

⇒a12=5+33

⇒a12=38

Thus 38 is the 12th term.