Question

65th terms in the sequence 8, 5, 2, -1

Answer 1

Question :-

Find 65ᵗʰterm in the sequence 8,5,2,-1 ...

Answer

The 65ᵗʰ term of the A.P. is -184.

Step-by-step explanation:

To Find :-

The 65ᵗʰ term of A.P. 8, 5, 2, -1

★ Solution

Given Arithmetic progression,

• 8, 5, 2, -1 . . . . . . .

Finding,

First term and common difference of the A.P. :-

First term = 8

And

Now, Common difference :-

→ 5 - 8 = -3

→ 2 - 5 = -3

→ -1 - 2 = -3

Hence, The common difference is -3.

Now, A . T . Q,

• The 65ᵗʰ is :-

We know,

tₙ = a + (n - 1)d,

Where,

• tₙ = nth term
• a = first term
• n = number of terms
• d = Common difference

Therefore,

⇒ tₙ = a + (n - 1)d

⇒ t₆₅ = 8 + (65 - 1)-3

⇒ t₆₅ = 8 + 64*-3

⇒ t₆₅ = 8 + (-192)

⇒ t₆₅ = 8 - 192

⇒ t₆₅ = -184

Hence, The 65ᵗʰ term of A.P. is -184.