Math, asked by shethdharmik002, 21 days ago

three num
bers are in an ap and their sum is 21 if the first and second are decreased by1 and third is increased by 7 they form a G.P find the three numbers in an Ap​

Answers

Answered by satishsharma88934
0

Answer:

Write sentences in your notebook to illustrate the following aspects of the possessive forms of the nouns.

Answered by shalinikk212000
0

Answer:

Let the first term of an A.P. be ‘a’ and its common difference be‘d’.

a1 + a2 + a3 = 21

Where, the three number are: a, a + d, and a + 2d

So,

3a + 3d = 21 or

a + d = 7.

d = 7 – a …. (i)

Now, according to the question:

a, a + d – 1, and a + 2d + 1

they are now in GP, that is:

(a + d - 1)/a = (a + 2d + 1)/(a + d - 1)

(a + d – 1)2 = a(a + 2d + 1)

a2 + d2 + 1 + 2ad – 2d – 2a = a2 + a + 2da

(7 – a)2 – 3a + 1 – 2(7 – a) = 0

49 + a2 – 14a – 3a + 1 – 14 + 2a = 0

a2 – 15a + 36 = 0

a2 – 12a – 3a + 36 = 0

a(a – 12) – 3(a – 12) = 0

a = 3 or a = 12

d = 7 – a

d = 7 – 3 or d = 7 – 12

d = 4 or – 5

Then,

For a = 3 and d = 4, the A.P is 3, 7, 11

For a = 12 and d = -5, the A.P is 12, 7, 2

∴ The numbers are 3, 7, 11 or 12, 7, 2

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