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1 of 2

Arithmetic

Progressions

Sums based on a_nand S_n formula

2 of 2

(ix) Given a₃ = 15, S₁₀ = 125, find d and a₁₀.

Sol:

a₃ = 15,

S₁₀ = 125

a₃ = a + 2d

∴

15 = a + 2d

∴

a + 2d = 15

….. (i)

S_n =

S₁₀ =

125 =

∴

=

∴

=

∴

Multiplying (i) by 2

∴

2a + 4d = 30

…(iii)

Subtracting (iii) from (ii)

2a

+

9d

= 25

2a

+

4d

= 30

(-)

(-)

(-)

5d

= – 5

∴

d

∴

d

Substituting value of d in (i)

a + 2

(– 1)

= 15

∴

a – 2

= 15

∴

a

= 15 + 2

∴

a

= 17

a₁₀

= a + 9d

∴

a₁₀

= 17 + 9(–1)

∴

a₁₀

= 17 – 9

∴

a₁₀

= 8

∴

d = –1, a₁₀ = 8

For given value of a₃. Let’s use the formula

For given value of S₁₀ Let’s use the formula

Substitute n = 10

Equation (i) and (ii) form pair of linear equations

Coefficients of none

Of the variables are same

We will make coefficient of variable ‘a’ same

Same coefficient and same sign

3) In an AP.

Lets find value of a₁₀

Exercise 5.3 3(iv)