Question

Which term of A. P. 9,12,15,....is 132

Answer 1

Answer :- 42th term

Given :-

◉ AP = 9,12,15,...

To Find :-

◉ Which term of the given AP is 132?

Solution :-

Given, AP = 9,12,15,...

Common difference, d = second term - last term = third term - second term

⇒ d = 12 - 9 = 15 - 12

⇒ d = 3

We got the common difference, d as 3

Now, Let assume that nth term of AP is 132, we need to find the value of n,

So,

In the AP:

• First term, a = 9
• Common difference, d = 3

⇒ Nth-term = a + (n - 1)d

⇒ 9 + (n - 1)3 = 132

⇒ 9 + 3n - 3 = 132

⇒ 3n = 132 - 6

⇒ 3n = 126

⇒ n = 42

Hence, 42th term of the AP is 132.

Some Formulae and Information :-

◉ An AP is a sequence of numbers in which the difference between two consecutive number is same.

For Example :-

• 2,4,6,8,10
• 1,2,3,4,5,6

◉ Nth term of from the last term:

nth term from the last term = a + (l - 1)d

Where,

• l = Number of terms in AP

◉ Sum of first n terms of an AP :-

Sn = n/2 [ 2a + (n - 1)s ]

Answer 2

Given ,

First term (a) = 9

Common difference (d) = 3

We know that , the nth term of an AP is given by

$\boxed{ \sf{a_{n} = a + (n - 1)d} }$

Thus ,

$\sf \mapsto 132 = 9 + (n - 1)3 \\ \\\sf \mapsto 123 = (n - 1)3 \\ \\\sf \mapsto 41 = n - 1 \\ \\ \sf \mapsto n = 42$

$\sf \therefore \underline{The \: number \: of \: terms \: is \: 42}$