Question

Given S = n/2 [2a + (n - 1)d], find d when S = 800,
n = 16, and a = 5.​

Answer 1

Answer:

d = 6

Step-by-step explanation:

sloving the given values

800 = 16/2 [ 2(5) + (16 - 1 ) d]

800 = 8 [ 10 + (15)d]

800 = 80 + 120d

120d = 800 - 80

120d = 720

therefore dividing the numbers we get the value if d ,

d = 720/120

d = 6

U can recheck your answer by solving the obtained value.

Answer 2

Given:

• Sn = Sum of n terms = 800
• n = number of terms = 16
• a = first term = 5

To find:

• d = common difference = ?

Method:

$\sf{s _{n}} = \frac{n}{2} (2a + (n - 1)d) \\ \\ Substitute \: values \\ \\ \implies \sf{800 = \frac{16}{2} (10 + (16 - 1)d } \\ \\ \implies \sf{800 = 8(10 + 15d) } \\ \\ \implies \sf{800 = 80 + 120d} \\ \\ \implies \sf{ {800-80} = 120d} \\ \\ \sf{720=120d} \\ \\ \therefore \sf{ \boxed{ \bf{d = 6}}}$

Therefore the common difference = 6

Additional information:

• an is the last term in the given Arithmetic Progression.
• an = a + (n - 1) d
• A set of numbers is said to be in Arithmetic Progression if it has a common difference that is 'd'