Question

The first the lost tems of an AP are 17 and 350 respectively . It the common difference is 9 how many tems are three is teir sum​

Answer 1

Answer:

ANSWER

Given

first term of A.P a

1

=17

last term of A.P a

n

=350

common difference d=9

the nth term of an A.P is given by

a

n

=a

1

+(n−1)d

for finding number of terms (n) put last term of A.P a

n

=350 in above equation

350=17+(n−1)9

17+9n−9=350

9n+8=350

n=

9

350−8

=

9

342

n=38

sum of n term of an A.P is given by .

S

n

=

2

n

(a

1

+a

n

)

⟹S

38

=

2

38

(17+350)

⟹S

38

=19×367

⟹S

38

=6973

hence number of terms in the A.P is n=38 and there sum is S

38

=6973

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
• $\sf a_{n} = 350$

$\sf : \implies S_{38} = \dfrac{\cancel{38}^{19}}{\cancel{2}} ( 17 + 350 )$

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

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

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

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

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