Arithmetic Progressions
Class 10 NCERT Exemplar Chapter Solutions
Q 1(MCQ): In an AP, if d=-4,an=7 and an=4, then a is equal to
(a) 6
(b) 7
(c) 20
(d) 28
Answer: (d) In an AP, an=a+(n-1)d
⇒ 4=a+(7-1) (-4)
⇒ 4=a+6(-4)
⇒ 4+24=a
∴ a=28
Q 2(mcq): In an AP, if a=3.5,d=0 and n=101, then an will be
(a) 0
(b) 3.5
(c) 103.5
(d) 104.5
Answer: (b) 3.5
For an AP, an =a+(n-1)d=3.5+(101-1)×0
∴ =3.5
Q 3(mcq): The list of numbers are -10,-6,-2,2,.... is
(a) an AP with d=-16
(b) an AP with d=4
(c) an AP with d=-4
(d) not an AP
Answer: (b) The given numbers are -10,-6,-2,2...is
Here, a1 = -10,
a2 = -6,
a3 = -2
and a4 =2...
Since, a2 - a1 = -6-(-10)
= -6+10=4
a3-a2= -2-(-6)
=-2+6=4
a4-a3=2-(-2)
=2+2=4
Each successive term of given list has the same difference i.e.,4.
So, the given list forms an AP with common difference, d=4.
Q 4(mcq): The first four terms of an AP whose first term is -2 and the common difference is -2 are
(a) -2,0,2,4
(b) -2,4,-8,16
(c) -2,-4,-6,-8
(d) -2,-4,-8,-16
Answer: (c) -2,-4,-6,-8
Let the first four terms of an AP are a,a+d,a+2d and a+3d.
Given, that first term, a=-2 and common difference, d=-2, then we have an AP as follows
-2,-2,-2,-2+2(-2),-2+3(-2)
= -2,-4,-6,-8