Question

Find whether 55 is a term of the A.P. 7, 10, 13, ... or not. If yes, find which term
is it.
​

Answer 1

Answer:

The 17ᵗʰ term of the A.P is 55.

Step-by-step-explanation:

The given arithmetic progression is 7, 10, 13, ...

• a = t₁ = 7
• d = t₂ - t₁ = 10 - 7 = 3

We have to find whether 55 is a term of the A.P or not.

Now, we know that,

tₙ = a + ( n - 1 ) * d - - - - - [ Formula ]

⇒ 55 = 7 + ( n - 1 ) * 3

⇒ 55 - 7 = ( n - 1 ) * 3

⇒ ( n - 1 ) 3 = 48

⇒ n - 1 = 48 ÷ 3

⇒ n - 1 = 16

⇒ n = 16 + 1

⇒ n = 17

∴ The 17th term of the A.P is 55.

Answer 2

Given :-

AP 7,10,13

To Find :-

Whether  55 is a term of the A.P. 7, 10, 13, ... or not. If yes, find which term

is it.

Solution :-

At first we need to find Common difference

a₂ - a₁ = a₃ - a₂

10 - 7 = 13 - 10

3 = 3

Hence

Common difference = 3

Now

aₙ = a + (n - 1) d

aₙ = 7 + (n - 1) × 3

55 = 7 + (n - 1) × 3

55 - 7 = (n - 1) × 3

48 = 3n - 3

48 + 3 = 3n

51 = 3n

51/3 = n

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