Question

In an A.P if T8=15 then find S15.

Answer 1

Answer:

answer is 225

Step-by-step explanation:

t8= 15

=a+7d=15......eq..1

now s15=15/2(2a+14d)

=(15/2)×2(a+7d)

=(15/2)×2×15. (: by using eq...1)

= 225.

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Answer 2

As per the data given in the above question.

We have to find the the sum of 15th term.

Given,

8th Terms

$n = 8$

$T_8=15$

$n \: for \: sum = 15$

Step-by-step explanation:

• A sequence of numbers that has a fixed common difference between any two consecutive numbers is called an arithmetic progression (A.P.).

The Nth term Formula of an A.P.

$a_n= a+(n-1)d \: \: \: \: \: \: \: ....(1)$

we have ,

$a_8= 15 \: and \: n=8$

$a_8= a+(8-1)d$

$15 = a + 7d \: \: \: \: \: \: .....(2)$

Now ,

Formula of sum of n terms ,

$S_n= \frac{n}{2} (2a + (n - 1)d) \: \: \: \: ....(3)$

We have

$n=15$

$S_15= \frac{15}{2} (2a + (15 - 1)d)$

$S_15= \frac{15}{2} (2a + (14)d)$

Take out common 2

$S_15= \frac{15}{2} (2(a+7d)) \: \: \: \: \: \: (4)$

Now put the value from equation (2) in equation (4)

$S_15= \frac{15}{2} (2 \times 15)$

$S_15= \frac{15}{2} \times 30$

$S_15= 15 \times 15$

$S_15= 225$

Hence,

The sum of 15th terms is

$S_15= 225$

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