Respuesta :
The sum of the first 20 terms is 800 if the sum of the first 7 terms of an arithmetical progression is 98 and the sum of the first 12 terms is 288.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Let's suppose the first term of AP is a and common difference is d
Then the sum of the first 7 terms of an arithmetical progression is 98
[tex]\rm 98 = \dfrac{7}{2}(2a+(7-1)d)\\\\196 =14a +42d\\\\a + 3d = 14 \ ...(1)[/tex]
The first 12 terms is 288,
[tex]\rm 288 = \dfrac{12}{2}(2a+(12-1)d)\\\\288 =12a +66d \\\\ 2a + 11d = 48 \ ....(2)[/tex]
After solving equation (1) and (2), we get:
a = 2, and d = 4
Then the sum of the first 20 terms is given by:
[tex]\rm S_2_0 = \dfrac{20}{2}(2(2)+(20-1)(4))[/tex]
[tex]\rm S_2_0 = \dfrac{20}{2}(4+76)[/tex]
[tex]\rm S_2_0 = 800[/tex]
Thus, the sum of the first 20 terms is 800 if the sum of the first 7 terms of an arithmetical progression is 98 and the sum of the first 12 terms is 288.
Learn more about the sequence here:
brainly.com/question/21961097
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