Class 10 Exam > Class 10 Tests > Assertion & Reason Test: Arithmetic Progressions - Class 10 MCQ

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Assertion & Reason Test: Arithmetic Progressions - Question 1

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): 184 is the 50^{th} term of the sequence 3, 7, 11, …………

Reason (R): The nth term of A.P. is given by a_{n} = a + (n – 1)d

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 1

Assertion & Reason Test: Arithmetic Progressions - Question 2

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Common difference of the A.P: -5,-1, 3, 7,……. is 4.

Reason (R): Common difference of the A.P. a, a + d, a + 2d, …….., is given by d = 2^{nd} term – 1^{st} term.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 2

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Assertion & Reason Test: Arithmetic Progressions - Question 3

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Sum of first hundred even natural numbers divisible by 5 is 500.

Reason (R): Sum of first n terms of an A.P is given l is last term

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 3

Assertion & Reason Test: Arithmetic Progressions - Question 4

Assertion (A): Sum of all 11 terms of an A.P whose middle most term is 30 is 330.

Reason (R): Sum of first n terms of an A.P is given by l is the middle term

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 4

Assertion & Reason Test: Arithmetic Progressions - Question 5

Assertion (A): If the n^{th} term of an A.P. is 7 – 4n, then its common differences is – 4.

Reason (R): Common differences of an A.P. is given by d = a_{n} + 1 – a_{n}

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 5

Assertion & Reason Test: Arithmetic Progressions - Question 6

Assertion (A): If five times the fifth term of an A.P. is equal to eight times its eighth term, then its 13th term is zero.

Reason (R): Common difference of the A.P. a, a + d, a + 2d, …….., is given by d = 2^{nd} term – 1^{st} term.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 6

Assertion & Reason Test: Arithmetic Progressions - Question 7

Assertion (A): There will be 10 rows in the flower bed if there are 23 plants in the first row, 21 in the second row, 19 in the third and so on. Also 5 rose plants are in the last row.

Reason (R): Sum of first n terms of an A.P is given by

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 7

Assertion & Reason Test: Arithmetic Progressions - Question 8

Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n^{2} – 4n. Then its n term is given by the term a_{n} = 6n – 7.

Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by a_{n} = S_{n} – S_{n} – 1

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 8

Assertion & Reason Test: Arithmetic Progressions - Question 9

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Common difference of the AP -5, -1, 3, 7, .......... is 4.

Reason : Common difference of the AP a,ad +a , d+ 2 , .......... is given by d = 2 nd term-1st term.

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 9

Assertion & Reason Test: Arithmetic Progressions - Question 10

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : a_{n} - a_{n} - 1 is not independent of n then the given sequence is an AP.

Reason : Common difference d =a_{n} - a_{n} - 1 is constant or independent of n .

Detailed Solution for Assertion & Reason Test: Arithmetic Progressions - Question 10

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