Question

the sum of an arithmatic series with 15 terms is 180. then the 8th term is​

Answer 1

Topic

Arithmetic Progression

Given

The sum of an Arithmetic Series with 15 terms is 180.

To Find

8th term of given AP.

Formula to be Used

Sₙ = [ n( 2a + ( n - 1 )d ) ] / 2

where

• S = Sum of n terms
• n = Number of terms
• a = first term
• d = common difference

Solving

It is given that

• S₁₅ = 180
• n = 15

Applying formula :-

S₁₅ = 15[ 2a + ( 15 - 1 )d ] / 2

180 = 15[ 2a + 14d ] / 2

(180 × 2) / 15 = [ 2a + 14d ]

24 = [ 2a + 14d ]

24/2 = a + 7d

12 = a + 7d

We know that :

nth term of an AP is

aₙ = a + ( n - 1 )d

So, 8th term will be

a₈ = a + ( 8 - 1 )d

a₈ = a + 7d

a + 7d = 12 then

a₈ = 12

Answer

8th term of given AP is 12.

Learn More :-

Arithmetic Progression ( AP )

A series with common difference between its consecutive terms is known as Arithmetic Progression.

Answer 2

Answer:

Question ---:

If the sum of the arithmetic series of 15 terms is 180, then what is the 8th term?

ANSWER :-

Whenever, an arithmetic series with odd number of terms is given, we can get the middle term by dividing the sum of terms by the number of terms. Therefore the middle term the 8th term is a and a = 180/15 = 12.

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