CBSE Class 10 Arithmetic Progression Printable Worksheet Set A

VERY SHORT ANSWER QUESTIONS(1 MARK)

Question. If the sum of first m terms of an AP is am2 + bm, find the common difference.
Answer : S_m= am² + bm, S₁= a+b= a₁, S₂ = 4a+2b= a₁+ a₂
a₂ = S₂- S₁= 4a+2b- (a+b) = 3a +b , d= a₂-a₁= 3a+b-(a+b)= 2a

Question. Three numbers are in AP and their sum is 24. Find the middle term.
Answer : Let the three numbers of the AP be a-d, a, a+d. So a-d +a+a+d= 24 ⟹ 3a=24,a=24/3=8. Hence the middle term =8.

Question. Find the sum of first 8 multiples of 3.
Answer : First 8 multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24 These numbers are in A.P.
where a = 3, d = 3 and n = 8 , a_n=24, S_n= 𝑛/2(a 1+ a_n), S₈= 8/2(3+ 24)= 4x27=108

Question. Find the sum: 34+ 32+30+……+10
Answer : Given, 34 + 32 + 30 + … + 10, first term, a = 34, d = a2−a1 = 32−34 = −2, Let 10 be the nth term of this A.P., an= a +(n−1)d, 10 = 34+(n−1)(−2), −24 = (n −1)(−2), 12 = n −1, n = 13, S_n = n/2 (a +l) , l = 10, S_n = n/2 (34 + 10) = 13/2 x44= 286

Question. Find the number of terms of an AP 5, 9,13, …, 185.
Answer : a₁=5, d=9-5=4, a_n=185, 185 = 5 + (n - 1)4, 185 = 5 + 4n -4,185 = 1 + 4n, 185 - 1 = 4n, 184 = 4n, n= 184/4 = 46

Question. Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5
Answer : Since, the number is divisible by both 2 and 5, means it must be divisible by 10.AP = 110, 120, 130,..., 990, a = 110, d = 10, nth term of the AP = 990
a+(n-1)d=990, 110+(n-1)10=990, (n-1)10=990-110,(n-1)= 880/10, n-1=88, n=88+1, n=89

Question. The fourth term of an AP is 11 and the eleventh term is 25. Determine the first term and common difference.
Answer : a + 3d = 11….(1) a + 10d = 25…..(2)
Subtracting equation (1) from equation (2 )
a + 10d – (a + 3d) = 25 – 11, 7d = 14, d = 2,
Putting value of d=2 in the equation 2,
a + 10x2 = 25, a + 20 = 25, a = 25 – 20, a = 5

Question. In an AP a = 15, d = -3, an = 0, then find the value of n.
Answer : First term (a) =15,Common difference (d) = -3,
Last term(an) = 0, 0 = 15 + (n - 1)-3 -15 = -3n + 3, -15 - 3 = -3n, -18 = -3n, n=6