Find the sum of first 15 terms of sequences having nth term as:xn = 6

1.	Find the sum of first 15 terms of sequences having nth term as:xn = 6 – n
Answer» Given an A.P. whose n^th term is given by x_n = 6 – n To find the sum of the n terms of the given A.P., using the formula S_n = \(\frac{n(a \,+\, l)}{2}\) Where, a = the first term l = the last term. Putting n = 1 in the given x_n, we get a = 6 – 1 = 5 For the last term (l), here n = 15 a₁₅ = 6 – 15 = -9 So, S_n = \(\frac{15(5 \,–\, 9)}{2}\) = 15 x (-2) = -30 Therefore, the sum of the 15 terms of the given A.P. is S₁₅ = -30

Find the sum of first 15 terms of sequences having nth term as:xn = 6 – n

Answer»

Given an A.P. whose n^th term is given by x_n = 6 – n

To find the sum of the n terms of the given A.P., using the formula

S_n = \(\frac{n(a \,+\, l)}{2}\)

Where, a = the first term l = the last term.

Putting n = 1 in the given x_n, we get

a = 6 – 1 = 5

For the last term (l), here n = 15

a₁₅ = 6 – 15 = -9

So, S_n = \(\frac{15(5 \,–\, 9)}{2}\)

= 15 x (-2)

= -30

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