Question

Find Sn for the arithmetic series 16+13+10 + … and determine the value of n for which
Sn= −6.

Answer 1

Answer:12

Step-by-step explanation:

Answer 2

The value of n for the series where $S_n = -6$ is 12.

• Given series is 16+13+10+...

Here.

First term (a) =16

Common difference (d) = 13-16 = -3

• Now the sum of n terms of an AP is given by the formula,

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

• Now , we have to find n for $S_n = -6$

• We substitute values in the formula,

$-6 = \frac{n}{2}[2(16)+(n-1)(-3)]$

$-6 = \frac{n}{2}[35 - 3n]$

-12 = n (35 - 3n)

3n² - 35n - 12 = 0

3n² - 36n + n - 12 = 0

3n(n-12) + 1(n-12) = 0

(n-12) (3n + 1) = 0

Therefore, n=12 and n=-1/3

• As n cannot be negative and in fraction , n=12 is the solution
• The value of n for which $S_n = -6$ is 12.