Question

Which term of the AP 7, 3, – 1, – 5, ... is – 153

Answer 1

Correct Question :-

Which term of A.P. is 7, 3, -1, -5, ... is -153.

Answer:-

The 41th term of AP - 7,3,-1,-5 .. is -153.

Step-by-step explanation

To Find :-

Which term of A.P. is -153.

★ Solution

Given Arithmetic progression [A.P.]

7, 3, -1, -5 ... ...

Firstly, Finding the first term and common difference of the given AP,

First term = 7.

Common difference :-

→ 3 - 7 = -4

→ 3 - (- 1) = -4

→ -5 - (-1) = -4

Hence, the common difference is -4.

______________________________

Now, According the question,

We know,

tₙ = a + (n - 1) d

Where,

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

Therefore, -153 = 7 + (n - 1) -4

⇒ -153 = 7 + (n - 1) -4

⇒ -153 = 7 + -4n + 4

⇒ -153 = 11 + (-4n)

⇒ -153 - 11 = -4n

⇒ -164 = -4n

⇒ -164/-4 = n

⇒ 164/4 = n

⇒ n = 41

Hence, The 41th term of AP is -153.