Question

Sum of 1st nine terms of an arithmetic sequence is 360 find the 5 the term

Answer 1

Answer:

s9 = 9/2(2a+8d)=360

2a+8d=80

a+4d=40

therefore , a5 = a+4d=40

Answer 2

The 5th term of AP = 40

Given:

Sum of 1st nine terms of an Arithmetic sequence = 360

To find:

The 5th term of the sequence

Solution:

As we know sum of the n terms in AP = $\frac{n}{2} [ 2a + (n-1)d ]$  

⇒ Sum of 9 terms = $\frac{9}{2} [ 2a + (9-1)d ]$  = $\frac{9}{2} [ 2a +8d ]$

From given data sum of 1st 9 terms = 360

⇒  $\frac{9}{2} [ 2a +8d ] = 360$

⇒ 9 [ 2a + 8d ] = 720

⇒  2a + 8d = 80

⇒ a + 4d = 40_(1)  [ divided by 2 ]  

As we know nth term of AP, a$_{n}$ = a + (n-1)d

⇒ 5th term of AP, a₅ = a + (5-1)d = a +4d

⇒ a₅ = a +4d _ (2)

From (1) and (2)

5th term of AP,  a₅ = 40

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