Question

the sum of an A.P with 15 term is 180 .then the 8 th term is
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Answer 1

Answer:

S15=180

=>n/2[2a+(n-1)d] = 180

=>15/2 [2a+(15-1)d] = 180

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

=>15[a+7d] = 180

=>a+7d = 180/15

=>a+7d = 12

=>a8 = 12

Hence, the 8th term is 12

Answer 2

The 8th term of the series is 12.

Given:

Number of terms in AP series = 15

Sum of AP series = 180

To Find:

The 8th term of the AP series.

Solution:

A sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value is called an Arithmetic Progression (AP) or Arithmetic Sequence.

The formula for finding the n-th term of an AP is:

aₙ = a + (n − 1) × d

Where,

a = First term

d = Common difference

n = number of terms

aₙ = nth term

Sₙ = $\frac{n}{2}$[2a + (n − 1) × d]

This is the AP sum formula to find the sum of n terms in a series (Sₙ).

According to the question,

Sₙ = 180

n = 15

Therefore,

$\implies S_{n} =\frac{n}{2} [2a+(n-1)d]\\\\\implies 180=\frac{15}{2} [2a+(15-1)d]\\\\\implies 180=\frac{15}{2} [2a+14d]\\\\\implies \frac{360}{15} = 2(a+14d)\\\\\implies \frac{360}{30} = (a+7d)\\\\\implies 12 = a+7d\\\\\implies 12 = a+(8-1)d\\\\\implies a+(8-1)d = 12$

Using the formula of n-th term, the 8th term of the series is 12.

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