Question 14

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Answer

Let A1, A2, A3, A4, and A5 be five numbers between 8 and 26 such that

8, A1, A2, A3, A4, A5, 26 is an A.P.

Here, *a *= 8, *b *= 26, *n* = 7

Therefore, 26 = 8 + (7 – 1) *d*

⇒ 6*d* = 26 – 8 = 18

⇒ *d *= 3

A1 = *a* + *d* = 8 + 3 = 11

A2 = *a* + 2*d* = 8 + 2 × 3 = 8 + 6 = 14

A3 = *a* + 3*d* = 8 + 3 × 3 = 8 + 9 = 17

A4 = *a* + 4*d *= 8 + 4 × 3 = 8 + 12 = 20

A5 = *a* + 5*d* = 8 + 5 × 3 = 8 + 15 = 23

Thus, the required five numbers between 8 and 26 are 11, 14, 17, 20, and 23.

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A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

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The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

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^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

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^{2}– 2 at x = 10. - Q:-
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.

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*m*+*n*)th and (*m*–*n*)th terms of an A.P. is equal to twice the*m**t*h term. - Q:-
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^{2}, ...ar^{n-1}and A, AR, AR^{2}, ,,,AR^{n-1 }form a G.P, and find the common ratio. - Q:-
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*p, q*and*r*terms of an A.P. are*a, b*and*c*, respectively.Prove that

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*x*-axis. What are its*y*-coordinates and*z*-coordinates? - Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.

- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

- Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER.

Ashish Kumar Pathak
2018-12-18 20:17:41

Thank you so much because this solution is given me a hot hint in my mind that help me in solving a lot of problems

Krithik
2018-08-24 19:06:03

Thanks this is very helpful to me Thank u so much

Pawankumar
2018-07-26 15:36:37

Give answer in Hindi

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