# Find the Sum of the First 15 Terms of Each of the Following Sequences Having Nth Term As Xn = 6 − N . - Mathematics

Find the sum of the first 15 terms of each of the following sequences having nth term as  xn = 6 − n .

#### Solution

Here, we are given an A.P. whose nth term is given by the following expression,  xn = 6 - n . We need to find the sum of first 15 terms.

So, here we can find the sum of the n terms of the given A.P., using the formula,

S_n = (n/2) (a + l)

Where, a = the first term

l = the last term

So, for the given A.P,

The first term (a) will be calculated using n = 1 in the given equation for nth term of A.P.

x = 6 -1

= 5

Now, the last term (l) or the nth term is given

l = an = 6 - n

So, on substituting the values in the formula for the sum of n terms of an A.P., we get,

S_15 = (15/2) [(5) + 6 - 15]

= (15/2) [11-15]

=(15/2) (-4)

= (15)(-2)

= - 30

Therefore, the sum of the 15 terms of the given A.P. is S15 = - 30.

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 5.3 | Page 51