The sum of its first twenty terms is 670 if the sum of the first 10 terms of an ap is 185. If it's last term is 4 times of the second term.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have the sum of the first 10 terms of an ap is 185. If it's last term is 4 times of the second term.
Let's suppose the common difference of an AP is d and the first term is 'a'.
185 = (10/2)[2a + (10-1)d]
185 = 5[2a + 9d]
37 = 2a + 9d ...(1)
a(10) = 4a(2) (last term is 4 times of the second term)
a + (10 - 1)d = 4(a + d)
a + 9d = 4a + 4d
3a - 5d = 0 ...(2)
After solving equation (1) and (2) we get:
a = 5
d = 3
The sum of the first 20 terms:
S(20) = (20/2)[2×5 + (20-1)3]
S(20) = 10[10 + 57]
S(20) = 670
Thus, the sum of its first twenty terms is 670 if the sum of the first 10 terms of an ap is 185. If it's last term is 4 times of the second term.
Learn more about the sequence here:
brainly.com/question/21961097
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