There are five terms in an Arithmetic Progression. The sum of these terms
is 55, and the fourth term is five more than the sum of the first two terms.
Find the terms of the Arithmetic progression.
3
Answers
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9
Answer:
3, 7, 11, 15, 19
Step-by-step explanation:
let the five terms of the AP be
(a-2d), (a-d), a, (a+d), (a+2d)
sum of the five terms is 55
a - 2d + a - d + a + a + d + a + 2d = 55
5a = 55
a = 55/5
a = 11
4th term is 5 more than sum of first two terms
a + d = a - 2d + a - d + 5
a + d = 2a - 3d + 5
11 + d = 2(11) - 3d + 5
11 + d = 22 - 3d + 5
11 + d = 27 - 3d
d + 3d = 27 - 11
4d = 16
d = 16/4
d = 4
the terms are
a - 2d = 11 - 2(4) = 11 - 8 = 3
a - d = 11 - 4 = 7
a = 11
a + d = 11 + 4 = 15
a + 2d = 11 + 2(4) = 11 + 8 = 19
the AP is 3, 7, 11, 15, 19
hope you get your answer
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