Question

What must be subtracted from 5n² - 18n + 30 to get 2n² + 4n + 23?

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Answer 1

Answer:

Let the number to be subtracted from each term be x

According to the question

33−x

17−x

=

15

7

255−15x=231−7x

15x−7x=255−231

8x=24

x=3

Therefore, 3 to be sutracted from each term of the ratio 17:30 so that the ratio becomes 7:15

Answer 2

Answer:

Let a be the first term and d be the common difference of an A.P. then sum

of n terms (Sn) = n/2.[2.a+(n-1).d].

S14= -203…………..(1)

14/2[2a+(14–1).d]= -203

2a+13d= - 29………….(2)

S25-S14 = -572……….(3). putting S14= -203 in eqn. (3)

S25+203 = -572

S25= -775

25/2[2a+(25–1)d] = -775

2a+24d=-775×2/25= - 31×2

2a+24d = -62………….(4).

Subtracting eqn. (2) from eqn. (4)

11d= -33. => d=-3. and. 2a -39=-29. =>. a= 5

Thus , the A.P. is:-

5 , 2 , -1 , -4 , -7 , -10 ,………………. Answer.