Question

The first and the last term of an A.P are 17 and 350 respectively. If the common difference is 9 how many terms are there in A.P?

Answer 1

Given:

• 1st Term = a = 17
• Last term = $a_n$= l = 350
• Common difference = d = 9

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Need to find:

• No of terms are there in that AP = n =?

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Solution:

We know,

$a_n$= a + ( n- 1 ) d

The last term of the AP:

→ a + ( n - 1 ) d = 350

Substituting the values we get,

→ 17 + ( n - 1)× 9 = 350

→ (n -1 )×9 = 350 - 17

→(n -1)×9 = 333

→ n - 1 = 333÷ 9

→ n -1 = 37

→n = 37 + 1

$\red{\large{\bold{\boxed{\implies n= 38}}}}$

∴ Number of terms in given AP is 38.

Answer 2

Given :

• First term, a = 17
• Last term, l = 350
• Common difference, d = 9

To find :

Number of terms in AP, n = ?

Solution :

Let, l be the nth term of AP.

$\sf : \implies a_{n} = l = 350$

Now, we know that :

$\Large \underline{\boxed{\bf{ a_{n} = a + ( n - 1 ) d }}}$

By, putting values,

$\sf : \implies 350 = 17 + ( n - 1 ) \times 9$

$\sf : \implies 350 = 17 + 9n - 9$

$\sf : \implies 350 = 8 + 9n$

$\sf : \implies 350 - 8 = 9n$

$\sf : \implies 342 = 9n$

$\sf : \implies \dfrac{ \cancel{342}^{38}}{\cancel{9}} = n$

$\sf : \implies 38 = n$

$\sf : \implies n = 38$

$\large \underline{\boxed{\sf n = 38}}$

Hence, There are 38 number of terms in given AP.