EduSahara™ Assignment
Name : Arithmetic Progressions Miscellaneous
Chapter : Arthimetic Progressions
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
The
t
15
of an A.P. is
43
and the
t
14
is
40
.
Find
t
11
.
(i)
32
(ii)
30
(iii)
28
(iv)
31
(v)
33
Question
2
2.
The
t
9
of an A.P. is
74
21
and the
t
5
is
46
21
.
Find
t
14
.
(i)
109
21
(ii)
37
7
(iii)
107
21
(iv)
109
19
(v)
109
23
Question
3
3.
Find the sum of first 81 natural numbers
(i)
3318
(ii)
3322
(iii)
3320
(iv)
3321
(v)
3323
Question
4
4.
Find the next
4
terms of the following A.P.
(
−
9
a
−
4
b
)
,
(
−
6
a
+
b
)
,
(
−
3
a
+
6
b
)
,
. . .
(i)
(
−
12
a
+
2
b
)
,
(
−
9
a
+
7
b
)
,
(
−
6
a
+
12
b
)
,
(
−
3
a
+
17
b
)
(ii)
(
3
a
+
16
b
)
,
(
6
a
+
21
b
)
,
(
9
a
+
26
b
)
,
(
12
a
+
31
b
)
(iii)
(
9
a
+
15
b
)
,
(
12
a
+
20
b
)
,
(
15
a
+
25
b
)
,
(
18
a
+
30
b
)
(iv)
(
−
9
a
+
7
b
)
,
(
−
6
a
+
12
b
)
,
(
−
3
a
+
17
b
)
,
22
b
(v)
11
b
,
(
3
a
+
16
b
)
,
(
6
a
+
21
b
)
,
(
9
a
+
26
b
)
Question
5
5.
Find
t
n
of the A.P
4
,
11
,
18
,
25
,
32
,
. . .
(i)
(
8
n
−
3
)
(ii)
(
7
n
+
1
)
(iii)
(
7
n
+
4
)
(iv)
(
4
n
−
3
)
(v)
(
7
n
−
3
)
Question
6
6.
Find
t
n
of the A.P
1
7
,
11
28
,
9
14
,
25
28
,
8
7
,
. . .
(i)
(
1
4
n
+
1
28
)
(ii)
(
13
4
n
−
3
28
)
(iii)
(
1
4
n
−
3
28
)
(iv)
(
−
3
4
n
−
3
28
)
(v)
(
1
4
n
+
1
7
)
Question
7
7.
The
t
2
of an A.P is
p
and
t
3
is
q
.
Find
t
17
and
t
n
.
(i)
(
−
14
p
+
15
q
)
,
(
−
p
n
+
3
p
+
q
n
−
2
q
)
(ii)
(
−
12
p
+
14
q
)
,
(
−
p
n
+
5
p
+
q
n
−
3
q
)
(iii)
(
−
15
p
+
16
q
)
,
(
−
p
n
+
2
p
+
q
n
−
q
)
(iv)
(
−
14
p
+
15
q
)
,
(
−
p
n
+
p
+
q
n
−
q
)
(v)
(
−
13
p
+
14
q
)
,
(
−
p
n
+
3
p
+
q
n
−
2
q
)
Question
8
8.
Determine k so that
(
5
k
+
2
)
,
(
2
k
+
8
)
and
(
6
k
+
1
)
are the consecutive terms of an A.P
(i)
15
7
(ii)
11
5
(iii)
5
3
(iv)
11
7
(v)
13
7
Question
9
9.
The product of two numbers is
5313
and their arithmetic mean is
73
.
Find the two numbers.
(i)
(
70
,
78
)
(ii)
(
69
,
76
)
(iii)
(
72
,
77
)
(iv)
(
79
,
71
)
(v)
(
69
,
77
)
Question
10
10.
Find the sum of all natural numbers between 1 and 100 which are multiples of 8?
(i)
624
(ii)
623
(iii)
627
(iv)
625
(v)
622
Question
11
11.
Find the sum of all natural numbers between 100 and 200 which are multiples of 5?
(i)
2849
(ii)
2851
(iii)
2847
(iv)
2850
(v)
2853
Question
12
12.
Find the sum of the following A.P. series
(
8
x
+
9
y
)
,
(
x
+
11
y
)
,
(
−
6
x
+
13
y
)
. . .
to
13
terms
(i)
(
−
442
x
+
273
y
)
(ii)
(
−
373
x
+
242
y
)
(iii)
(
−
359
x
+
238
y
)
(iv)
(
−
523
x
+
172
y
)
(v)
(
−
539
x
+
154
y
)
Question
13
13.
Find
t
n
of the A.P
2
,
5
,
8
,
. . .
(i)
(
3
n
−
1
)
(ii)
(
n
−
1
)
(iii)
(
3
n
+
1
)
(iv)
(
3
n
+
2
)
(v)
(
7
n
−
1
)
Question
14
14.
If
S
70
and
S
90
of an A.P. are
5110
and
8370
respectively, then
S
160
=
(i)
26083
(ii)
26081
(iii)
26077
(iv)
26080
Question
15
15.
If x
≠
y and the sequences x ,
a
1
,
a
2
, y and x ,
b
1
,
b
2
, y
each are in A.P., then
a
2
−
a
1
b
2
−
b
1
=
(i)
(
-3
4
)
(ii)
4
3
(iii)
2
3
(iv)
1
(v)
3
2
Question
16
16.
If there are n arithmetic means between a and b, the common difference d =
(i)
(
n
−
1
)
(
a
+
b
)
(ii)
(
b
−
a
)
(
n
+
1
)
(iii)
(
a
−
b
)
(
n
+
1
)
(iv)
(
b
−
a
)
(
n
−
1
)
(v)
(
a
+
b
)
(
n
+
1
)
Question
17
17.
The sum of first n natural number is
(i)
n
2
(
n
+
1
)
2
4
(ii)
(
n
)
(
n
+
1
)
2
(iii)
(
n
)
(
n
−
1
)
2
(iv)
(
n
)
(
n
+
1
)
(
2
n
+
1
)
6
(v)
(
n
−
1
)
(
n
+
1
)
2
Question
18
18.
The measures of the interior angles of a convex polygon are in A.P.
If the smallest angle is
87
and the largest angle is
129
,
then the number of sides of the polygon is
(i)
3
(ii)
6
(iii)
4
(iv)
7
(v)
5
Question
19
19.
If the
t
n
of an A.P is
(
3
n
+
5
)
, find
S
n
(i)
(
7
)
(
n
2
+
n
)
2
+
5
n
(ii)
(
5
)
(
n
2
+
n
)
2
+
2
n
(iii)
(
3
)
(
n
2
+
n
)
2
+
5
n
(iv)
(
2
)
(
n
2
+
n
)
2
+
n
(v)
(
9
)
(
n
2
+
n
)
2
+
9
n
Question
20
20.
Determine
t
10
and
t
n
of an A.P. whose
t
9
is
75
and
t
6
is
48
.
(i)
83
;
(
9
n
+
3
)
(ii)
86
;
(
13
n
−
6
)
(iii)
84
;
(
9
n
−
6
)
(iv)
82
;
(
6
n
−
6
)
(v)
85
;
(
9
n
−
3
)
Assignment Key
1) (iv)
2) (i)
3) (iv)
4) (v)
5) (v)
6) (iii)
7) (i)
8) (v)
9) (v)
10) (i)
11) (iv)
12) (i)
13) (i)
14) (iv)
15) (iv)
16) (ii)
17) (ii)
18) (v)
19) (iii)
20) (iii)
