EduSahara™ Assignment
Name : Arithmetic Progressions Miscellaneous
Chapter : Arthimetic Progressions
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
The
t
16
of an A.P. is
109
and the
t
5
is
32
.
Find
t
11
.
(i)
75
(ii)
72
(iii)
76
(iv)
74
(v)
73
Question
2
2.
The
t
9
of an A.P. is
19
6
and the
t
7
is
5
2
.
Find
t
5
.
(i)
11
6
(ii)
11
4
(iii)
3
2
(iv)
13
6
(v)
11
8
Question
3
3.
Find the sum of first 52 natural numbers
(i)
1379
(ii)
1380
(iii)
1377
(iv)
1378
(v)
1375
Question
4
4.
Find the next
4
terms of the following A.P.
(
3
a
−
2
b
)
,
(
−
2
a
+
7
b
)
,
(
−
7
a
+
16
b
)
,
. . .
(i)
(
−
9
a
+
23
b
)
,
(
−
14
a
+
32
b
)
,
(
−
19
a
+
41
b
)
,
(
−
24
a
+
50
b
)
(ii)
(
−
17
a
+
34
b
)
,
(
−
22
a
+
43
b
)
,
(
−
27
a
+
52
b
)
,
(
−
32
a
+
61
b
)
(iii)
(
−
12
a
+
25
b
)
,
(
−
17
a
+
34
b
)
,
(
−
22
a
+
43
b
)
,
(
−
27
a
+
52
b
)
(iv)
(
−
4
a
+
14
b
)
,
(
−
9
a
+
23
b
)
,
(
−
14
a
+
32
b
)
,
(
−
19
a
+
41
b
)
(v)
(
−
15
a
+
27
b
)
,
(
−
20
a
+
36
b
)
,
(
−
25
a
+
45
b
)
,
(
−
30
a
+
54
b
)
Question
5
5.
Find
t
n
of the A.P
9
,
14
,
19
,
24
,
29
,
. . .
(i)
(
5
n
+
13
)
(ii)
(
5
n
+
4
)
(iii)
(
8
n
+
4
)
(iv)
(
3
n
+
4
)
(v)
(
5
n
+
9
)
Question
6
6.
Find
t
n
of the A.P
2
9
,
5
9
,
8
9
,
11
9
,
14
9
,
. . .
(i)
(
1
3
n
+
2
9
)
(ii)
(
1
3
n
−
1
9
)
(iii)
(
−
5
3
n
−
1
9
)
(iv)
(
1
3
n
+
1
9
)
(v)
(
10
3
n
−
1
9
)
Question
7
7.
The
t
5
of an A.P is
p
and
t
6
is
q
.
Find
t
13
and
t
n
.
(i)
(
−
8
p
+
9
q
)
,
(
−
p
n
+
5
p
+
q
n
−
4
q
)
(ii)
(
−
7
p
+
8
q
)
,
(
−
p
n
+
6
p
+
q
n
−
5
q
)
(iii)
(
−
7
p
+
8
q
)
,
(
−
p
n
+
p
+
q
n
−
q
)
(iv)
(
−
6
p
+
7
q
)
,
(
−
p
n
+
6
p
+
q
n
−
5
q
)
(v)
(
−
2
p
+
4
q
)
,
(
−
p
n
+
11
p
+
q
n
−
9
q
)
Question
8
8.
Determine k so that
(
7
k
+
2
)
,
(
6
k
+
5
)
and
(
7
k
+
8
)
are the consecutive terms of an A.P
(i)
-3
(ii)
1
(iii)
0
(iv)
3
(v)
-1
Question
9
9.
The product of two numbers is
6660
and their arithmetic mean is
82
.
Find the two numbers.
(i)
(
74
,
90
)
(ii)
(
74
,
89
)
(iii)
(
76
,
90
)
(iv)
(
92
,
76
)
(v)
(
75
,
91
)
Question
10
10.
Find the sum of all natural numbers between 1 and 100 which are multiples of 9?
(i)
595
(ii)
596
(iii)
593
(iv)
594
(v)
591
Question
11
11.
Find the sum of all natural numbers between 100 and 200 which are multiples of 5?
(i)
2852
(ii)
2850
(iii)
2847
(iv)
2851
(v)
2849
Question
12
12.
Find the sum of the following A.P. series
(
7
x
+
8
y
)
,
(
16
x
+
7
y
)
,
(
25
x
+
6
y
)
. . .
to
11
terms
(i)
(
466
x
+
36
y
)
(ii)
(
486
x
−
54
y
)
(iii)
(
484
x
+
34
y
)
(iv)
(
572
x
+
33
y
)
(v)
(
500
x
−
38
y
)
Question
13
13.
Find
t
n
of the A.P
5
,
7
,
9
,
. . .
(i)
(
2
n
+
8
)
(ii)
(
4
n
+
3
)
(iii)
(
n
+
3
)
(iv)
(
2
n
+
5
)
(v)
(
2
n
+
3
)
Question
14
14.
If
S
80
and
S
90
of an A.P. are
19440
and
24570
respectively, then
S
170
=
(i)
87208
(ii)
87210
(iii)
87213
(iv)
87211
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)
1
(ii)
2
3
(iii)
3
2
(iv)
4
3
(v)
(
-3
4
)
Question
16
16.
If there are n arithmetic means between a and b, the common difference d =
(i)
(
a
+
b
)
(
n
+
1
)
(ii)
(
b
−
a
)
(
n
+
1
)
(iii)
(
a
−
b
)
(
n
+
1
)
(iv)
(
n
−
1
)
(
a
+
b
)
(v)
(
b
−
a
)
(
n
−
1
)
Question
17
17.
The sum of first n natural number is
(i)
(
n
)
(
n
+
1
)
(
2
n
+
1
)
6
(ii)
(
n
)
(
n
+
1
)
2
(iii)
(
n
−
1
)
(
n
+
1
)
2
(iv)
n
2
(
n
+
1
)
2
4
(v)
(
n
)
(
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
126
and the largest angle is
144
,
then the number of sides of the polygon is
(i)
9
(ii)
8
(iii)
11
(iv)
7
(v)
5
Question
19
19.
If the
t
n
of an A.P is
(
4
n
+
6
)
, find
S
n
(i)
(
2
)
(
n
2
+
n
)
2
+
n
(ii)
(
4
)
(
n
2
+
n
)
2
+
6
n
(iii)
(
7
)
(
n
2
+
n
)
2
+
5
n
(iv)
(
8
)
(
n
2
+
n
)
2
+
n
(v)
(
8
)
(
n
2
+
n
)
2
+
8
n
Question
20
20.
Determine
t
8
and
t
n
of an A.P. whose
t
10
is
77
and
t
2
is
13
.
(i)
59
;
(
7
n
−
3
)
(ii)
61
;
(
8
n
−
3
)
(iii)
60
;
(
8
n
+
5
)
(iv)
63
;
(
11
n
−
3
)
(v)
62
;
(
8
n
+
2
)
Assignment Key
1) (iv)
2) (i)
3) (iv)
4) (iii)
5) (ii)
6) (ii)
7) (ii)
8) (iii)
9) (i)
10) (iv)
11) (ii)
12) (iv)
13) (v)
14) (ii)
15) (i)
16) (ii)
17) (ii)
18) (ii)
19) (ii)
20) (ii)
