Sum of the four terms of an arithmetic progression is 68 and the product of middle
two terms is 280. Find the four terms.
Answers
Answer:
8,14,20,26
Step-by-step explanation:
hope this help...u can also fond the terms by taking D as-3
The four terms of arithmetic progression are 8, 14, 20 and 26.
Step-by-step explanation:
Let the four terms in arithmetic progression are (a - d), a, (a + d), (a + 2d).
Sum of four terms of an arithmetic progression = 68
=> a - d + a + a + d + a + 2d = 68
=> 4a + 2d = 68
=> 2a + d = 34.........................(i)
Product of middle two terms = 280
=> a(a + d) = 280
Now, use equation(i), d = 34 - 2a
=> a(a + 34 - 2a) = 280
=> a(34 - a) = 280
=> 34a - - 280 = 0
=> - 34a + 280 = 0
=>
=> a(a - 14) - 20(a - 14) = 0
=> (a - 14)(a - 20) = 0
=> a = 14, 20
If a = 14 then d = 34 - 2 x 14 = 34 - 28 = 6.
If a = 20 then d = 34 - 2 x 20 = 34 - 40 = -6.
If a = 14 and d = 6,
four terms are a - d = 14 - 6 = 8
a = 14, a + d = 14 + 6 = 20, a + 2d = 14 + 2 x 6 = 14 + 12 = 26.
If a = 20 and d = -6,
four terms are a - d = 20 - (-6) = 26
a = 20, a + d = 20 - 6 = 14, a + 2d = 20 + 2 x (-6) = 20 - 12 = 8.
Hence, the four terms of arithmetic progression are 8, 14, 20 and 26.