Math, asked by srinthvn90p48ji8, 11 months ago


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

Answered by sara16105305
32

Answer:

8,14,20,26

Step-by-step explanation:

hope this help...u can also fond the terms by taking D as-3

Attachments:
Answered by harendrakumar4417
17

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 - a^{2} - 280 = 0

=> a^{2} - 34a + 280 = 0

=> a^{2} - 14a - 20a + 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.

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