Question

There are 37 terms in an A.P. the sum of three terms placed exactly in the middle is 225 and the sum of last three terms is 429. Write the A.P.
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Answer 1

Step-by-step explanation:

Let the first term be a and the common

difference be d.

Since, the A.P. contains 37 terms. the

middle term is

term.

(³7 + 1)

37+1

2

According to the question.

A18+ a19+ a20 225

⇒ (a +(18-1)d) + (a + (19 − 1)

3a + 17d18d 19d = 225

3a54d = 225

⇒ 3 (a + 18d) = 225

⇒ a 18d 225 3 -

a 18d:

→ a=75 -

75

18d

⇒ a 18d = 75

⇒a= 75 - 18d... (1)

Also.

a35a36 a37 = 429

⇒ (a + (35 - 1)d) + (a + (36 − 1)

3a34d35d +36d = 429

⇒ 3a+105d 429

3 (a +35d) = 429

429

⇒ a +35d 3

75 - 18d35d= 143 (from (

17d 143 75

⇒ 17d = 68

⇒ d = 4

z Orithmatic alom

⇒ 17d = 68

⇒ d 4

⇒a= 75 - 18 (4) (from (1))

⇒a= 75 - 72

⇒ A= 3

Hence, the resulting A.P is 3. 7. 11. ....

Concept M

f

Concept: Sum of First n Terms of an AP

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Chapter 3 Arithmetic Progression - Problem Set 3 [Page 80]

Q9

Casinoin Hey yaar, get

Q 10

To Play

Q 11

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Answer 2

Answer:

Heya Here's the required Answer mate

• Let the first term and the common difference of the A.P are a and d respectively.

• Since the A.P contains 37 terms. So, the middle most term is (37+1)/2 th term = 19th term.

• Thus, three middle most terms of this A.P.are 18th, 19th and 20th terms.

Given

• a 18 + a 19 + a 20 = 225

• ⇒ (a + 17d) + (a + 18d) + (a + 19d) = 225

• ⇒ 3(a + 18d) = 225

• ⇒ a + 18d = 75

• ⇒ a = 75 – 18d … (1)

According to given information

• a 35 + a 36 + a 37 = 429

• ⇒ (a + 34d) + (a + 35d) + (a + 36d) = 429

• ⇒ 3(a + 35d) = 429

• ⇒ (75 – 18d) + 35d = 143

• ⇒ 17d = 143 – 75 = 68

• ⇒ d = 4

Substituting the value of d in equation (1), it is obtained

• a = 75 – 18 × 4 = 3

Thus, the A.P. is 3, 7, 11, 15 ..., 147.

Hope it helps dear

Have a great day ahead