1 of 4

ARITHMETIC

PROGRESSIONS

  • Sums based on ‘an’ formula

2 of 4

1) Fill in the blanks in the following table, given that a is the first term,

d the common difference and an the nth term of the AP:

a

d

n

an

​

​

​

​

v) 3.5 0 105 …

Sol:

We need to find an

We know that,

an =

a + (n – 1) d

=

3.5

+ (105 – 1)

(0)

=

3.5 + 0

∴ an = 3.5

a

d

n

an

3.5

0

105

​

3.5

Exercise 5.2 1(v)

HOMEWORK

3 of 4

2) Choose the correct choice in the following and justify.

i) 30th term of AP: 10, 7, 4, …, is

(A) 97 (B) 77 (C) -77 (D) -87

a = 10,

Sol:

a30 =

a + 29 d

=

10 + 29(– 3)

=

10 – 87

=

– 77

∴ Option (C) is correct

d = 7 – 10

= – 3

We need to find a30

For the given AP

lets find value of a & d

Exercise 5.2 2(i)

HOMEWORK

4 of 4

2) Choose the correct choice in the following and justify.

 

(A) 28 (B) 22 (C) -38 (D) – 48

a = -3,

Sol:

d = – (-3)

= + 3

a11 =

a + 10 d

=

– 3 + 10 ×

=

– 3 + 25

=

22

5

∴ Option (B) is correct

For the given AP

lets find value of a & d

We need to find a11

Exercise 5.2 2(ii)

HOMEWORK