Question

If th 6 and th 15 terms of an AP are 22 and 49 respectively, then its th 20 term is​

Answer 1

a=3

d=7

a20=a+19d

= 3+19(7)

= 3+133

=136

so the 20th term is 136 ....

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Answer 2

Answer:

20th term of the A.P = 64

Step-by-step explanation:

Given:

• 6th term of the A.P = 22
• 15th term of the A.P = 49

To Find:

• The 20th term

Solution:

First we have to find the first term and common difference of the A.P

The 6th term of an A.P is given by,

a₆ = a₁ + (6 - 1) × d

a₁ + 5d = 22 ----(1)

The 15th term of the A.P is given by,

a₁₅ = a₁ + (15 - 1) × d

a₁₅ = a₁ + 14d

By given,

a₁ + 14d = 49-----(2)

Solving equation 1 and 2 by elimination method,

a₁ + 14d = 49

a₁ + 5d = 22

      9d = 27

        d = 27/9

        d = 3

Hence the common difference of the A.P is 3.

Substitute the value of d in equation 1

a₁ + 5 × 3 = 22

a₁ = 22 - 15

a₁ = 7

Hence the first term of the A.P is 7.

Now the 20th term of the A.P is given by,

a₂₀ = a₁ + 19d

Substituting the value,

a₂₀ = 7 + 19 × 3

a₂₀ = 7 + 57

a₂₀ = 64

Hence the 20th term of the A.P is 64.