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Arithmetic

Progressions

  • Sums based on an and Sn formula

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Q.7. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Sol:

For an A.P :

a22 = a + 21d

∴

149

= a + 21 × 7

∴

149

= a + 147

∴

149 –147

= a

∴

a

= 2

 

S22 =

 

S22 = 1661

For given value of a22

d = 7,

a22 = 149

Substitute,

d = 7 & a22 = 149

Substitute,

n = 22, a = 2 & a22 = 149

 

∴

Exercise 5.3 7

HOMEWORK

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Lets find S51

Q.8. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Sol:

For an A.P : a2 = 14, a3 = 18

d = a3 – a2

= 18 – 14

= 4

a2 = a + d

14 = a + 4

∴

14 – 4 = a

∴

a = 10

 

S51 =

 

 

 

∴

S51 = 5610

∴

Sum of first 51 terms is 5610

Substitute n = 51, a = 10 & d = 4

To find S51

To find S51 we need to find the value of a & d

∴

For given value of a2

[2(10)

+ (51 – 1)

4]

 

[ 20

+ (50)

4]

 

Exercise 5.3 8