Question

If the sum of first 15 terms of an A.P is 675 and its first term is 10.then find 25th term

Answer 1

Answer:

Step-by-step explanation:

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The sum of first 15 terms of an A.P. is 105 and the sum of next 15 terms is 780. Find the A. P.

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JUSTAGUIDE eNotes educator| CERTIFIED EDUCATOR

For an AP with first term a and the common difference d, the sum of the first n terms is given as (2a + (n-1)d)(n/2).

Now for the AP given the sum of the first 15 terms is 105

=> (2a + 14d)(15/2) = 105...(1)

The sum of the next 15 terms is the sum of the first 15 terms subtracted from the sum of the first 30 terms.

=> (2a + 29d)(30/2) - 105 = 780

=> (2a + 29d) = 885/15

=> (2a + 29d) = 59

(1)

=> (2a + 14d)(15/2) = 105

=> 2a + 14d = 14

2a + 29d - 2a - 14d = 59 - 14

=> 15d = 45

=> d = 3

2a + 14d = 14

=> 2a = 14 - 42

=> 2a = -28

=> a = -14

Therefore the AP has the first term as -14 and the common difference is 3.

Answer 2

The 25th term is 130

Step-by-step explanation:

First term of AP = a = 10

We are given that  sum of first 15 terms of an A.P is 675

Formula of sum of first n terms = $S_n=\frac{n}{2}(2a+(n-1)d)$

Substitute n = 15

$S_{15}=\frac{15}{2}(2(10)+(15-1)d)$

$\frac{15}{2}(2(10)+(15-1)d)= 675$

$7.5(20+14d)= 675$

$20+14d= \frac{675}{7.5}$

$14d= \frac{675}{7.5}-20$

$d=\frac{\frac{675}{7.5}-20}{14}$

d=5

Formula of nth term = $a_n=a+(n-1)d$

Substitute n = 25

a_{25}=10+(25-1)(5)

a_{25}=130

Hence The 25th term is 130

#Learn more:

Sum of the first 14 terms of an A.P is 1505 and it's first term is 10 . find its 25th term

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