Question

Find the number of terms in an A.P. 18,15,12,……., – 48 and also find the sum of all

of its terms.


please tell me fast​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The total number of terms is 23, and the sum of all of its terms is -345.

Given,

A.P. 18,15,12,      – 48

To Find,

The number of terms in the A.P. and the sum of all of its terms

Solution,

We can solve the question as follows:

It is asked that we have to find the number of terms in the given A.P. and also the sum of its terms.

$A.P. = 18,15,12,........ -48$

Since -48 is the last term, we can find the total number of terms by finding the nth position of -48.

The formula for finding the nth term of an A.P. is given as:

$T_{n} = a + (n - 1)d$

Where,

$T_{n}= nth\: term\\ a = first\: term\\d = common\: difference\\n = term\: position$

In the given question,

$T_{n} = 48\\a = 18$

The common difference is the difference between any two consecutive terms of an A.P. Therefore,

$Common\: difference = 15 - 18 = -3$

Substituting the values in the above formula,

$-48 = 18 + (n - 1)(-3)$

$-48 - 18 = -3n + 3$

$-66 = -3n + 3$

$-66 - 3 = -3n$

$69 = 3n$

$n = \frac{69}{3} = 23$

The total number of terms is 23.

Now, the sum of n terms of an A.P. is given as:

$S_{n} = \frac{n}{2} [2a + (n - 1)d]$

Where,

$S_{n} = Sum\: of\: n\: terms\\n = Total\: number\: of\: terms$

Substituting the values in the above formula,

$S_{23} = \frac{23}{2} [2*18 + (23 - 1)(-3)]$

     $= \frac{23}{2} [36 + (22)(-3)]$

     $= \frac{23}{2} [36 + -66]$

      $= \frac{23}{2}*(-30)$

      $= 23*-15 = -345$

Hence, the total number of terms is 23, and the sum of all of its terms is -345.