An arithmetic has 3 as it first term also the sum of the first 8 term is twice the sum of the 5 term. Find the common different?

1 Answer
Mar 6, 2017

Answer:

#d = 3/4#

Explanation:

We must write an equation using the formula #s_n = n/2(2a + (n - 1)d)#, in order to solve for #d#, the common difference.

We know that #s_8 = 2(s_5)#, and that #a = 3#, so our equation will be:

#8/2(2(3) + (8 - 1)d) = 2(5/2(2(3) + (5- 1)d))#

#4(6 + 7d) = 5(6 + 4d)#

#24 + 28d = 30 + 20d#

#24 - 30 = 20d - 28d#

#-6 = -8d#

#d = 3/4#

If you recheck using the formula #s_n = n/2(2a + (n - 1)d)#, you will find that #s_5 = 45/2# and #s_8 = 45#, which makes our answer correct (since #2s_5 = s_8#).

Hopefully this helps!