Question

The first and the last term of ap are 17 and 350 respectivily if the common differentce is 9 how many term are there and what is their sum​

Answer 1

Step-by-step explanation:

a=17

d=9

l= 350

l=a +(n-1)d

350 = 17+(n-1)9

333 = (n-1)9

37 = n-1

n = 38

Sn =n/2 {2a +(n-1)d}

= 38/2{2*17 +(38- 1) 9}

= 19{ 34+ 37*9}

= 19{ 34+ 333}

= 19 *367

=6973

Answer 2

Given:

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

To find:

• Number of terms = n
• Sum of all terms = Sn

Formulas used:

1) an = a + (n - 1)d

$\sf{2)s _{n} = \frac{n}{2} \times (a + a _{n}) }$

Proof:

an = a + (n - 1)d

⇒350 = 17 + (n - 1)9

⇒ 333 = (n - 1)9

⇒ n - 1 = 37

⇒ n = 38

∴ There are 38 terms

$\sf{s _{n} = \frac{n}{2} \times (a + a _{n}) }$

⇒Sn = ³⁸/₂ × (17 + 350)

⇒ Sn = 19 × 367

⇒ Sn = 6973

∴ Sum of all terms in given A.P = 6973