Question

The first and the last terms of an A.P. are 17 and 350
respectively. If the common difference is 9, how many
terms are there and what is their sum?​

Answer 1

Step-by-step explanation:

first term = a = 17

last term = l = 350

common difference = d = 9

an = a + (n-1)d

350 = 17 + (n-1)9

350 - 17 = (n-1)9

333 = (n-1)9

333/9 = n - 1

37 = n - 1

n = 37 + 1

n = 38

therefore the number of terms is 38

sum of all the terms

Sn = n/2 (a + l)

= 38/2 (17 + 350)

= 19 × 367

= 6973

hope you get your answer

Answer 2

Given :

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

To Find :

• Number of terms in AP, n = ?
• Sum of total number of terms in AP, $\sf S_{n} = ?$

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.

Now, let's find sum of total number of terms in AP.

We know that :

$\Large \underline{\boxed{\bf{ S_{n} = \dfrac{n}{2} ( a + a_{n}) }}}$

We have :

• n = 38
• a = 17
• $\sf a_{n} = 350$

$\sf : \implies S_{38} = \dfrac{\cancel{38}^{1}}{\cancel{2}} ( 17 + 350 )$

$\sf : \implies S_{38} = 19 (367)$

$\sf : \implies S_{38} = 19 \times 367$

$\sf : \implies S_{38} = 6973$

$\large \underline{\boxed{\sf S_{38} = 6973}}$

Hence, There are 38 number of terms in given AP and their sum is 6973.