Class 10 Maths Chapter 5 Assertion and Reason Questions - Arithmetic Progressions
Q1:
Assertion (A): 184 is the 50th term of the sequence 3, 7, 11, …………
Reason (R): The nth term of A.P. is given by an = a + (n – 1)d
Q2:
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 = 2nd term – 1st term.
Q3:
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
Q4:
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
is last term(Here we can’t apply this formula as no last term is mentioned in the statement.)Q5:
Assertion (A): If the nth 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 = an + 1 – an
Q6:
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 = 2nd term – 1st term.
Q7:
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 
Q8:
Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.
Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1
Q9:
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.
Q10:
Assertion : an - an - 1 is not independent of n then the given sequence is an AP.
Reason : Common difference d =an - an - 1 is constant or independent of n .
Q11:
Assertion : Three consecutive terms 2k +1, 3k+3and 5k -1 form an AP than k is equal to 6.
Reason : In an AP a,a +d , a+2d, .........., the sum to n terms of the AP be 
and d is constant.
Q12:
Assertion : The sum of the first n terms of an AP is given by Sn = 3n2 -4 . Then n its nth term an = 6n -7 .
Reason : n th term of an AP, whose sum to n terms is Sn , is given by an =Sn - Sn - 1
Q13:
Assertion : Common difference of an AP in which a21 -a7 = 84 is 14.
Reason : n th term of AP is given by an = a + (n - 1)d
Q14:
Assertion : Arithmetic between 8 and 12 is 10.
Reason : Arithmetic between two numbers ‘a ’ and 'b' is given as 
Q15:
Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
Q16:
Assertion : Sum of first 10 terms of the arithmetic progression - 0.5 , - 1.0, - 1.5 , .......... is -27.5
Reason : Sum of n terms of an A.P. is given as 
where a = first term, d = common difference.
Q17:
Assertion : The sum of the series with the nth term. tn = (9 - 5n) is (465), when no. of terms n = 15 .
Reason : Given series is in A.P. and sum of n terms of an A.P. is 
Q18:
Assertion : If n th term of an A.P. is 7 -4n , then its common differences is -4.
Reason : Common difference of an A.P. is given by d =an + 1 - an
Q19:
Assertion : If Sn is the sum of the first n terms of an A.P., then its nth term an is given by an =Sn - Sn - 1 .
Reason : The 10th term of the A.P. 5, 8, 11, 14, .......... is 35.
Q20:
Assertion : Sum of first hundred even natural numbers divisible by 5 is 500.
Reason : Sum of first n -terms of an A.P. is given by 
where ℓ = last term.
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