Question 2

Find the sum to *n* terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

Answer

The given series is 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

*n*th term, *a**n* = *n* ( *n* + 1) ( *n* + 2)

= (*n*^{2} + *n*) (*n* + 2)

= *n*^{3} + 3*n*^{2} + 2*n*

∴

- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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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.

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

- Q:-
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- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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

- 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:-
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- Q:-
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*n*. - Q:-
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- Q:-
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*a*and*b*, then find the value of*n*. - Q:-
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