Question

iii) For an A.P., the first term is a 5 and the last term is 30. The sum of all the terms is 420 what
is the value of n ?
(a) 12
b) 24
(c) 10
(d 20​

Answer 1

Answer:

24

Step-by-step explanation:

Let the common difference be d.

Using, a(n) = a + (n - 1)d      , where letters have their usual meaning.

⇒ 30 = 5 + (n - 1)d

⇒ 25 = (n - 1)d

Sum of n terms = (n/2) [2a + (n - 1)d]

            420 = (n/2) [2(5) + 25]

            24 = n

You can directly, use

 S = (n/2) [a + l],  where l is last term,

420 = (n/2) [5 + 30]  ⇒ 24 = n

Answer 2

Answer:

Given

• ➥ For an A.P., the first term is 5 and the last term is 30.
• ➥ The sum of all the terms is 420.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

To Find

• ➥ Value of n

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Using Formula

$: \implies\:{\sf{\pink{S_{n} =\purple{ \dfrac{n}{2} \Big(a + l \Big)}}}}$

Where

• ${ \leadsto\sf{S_n= Sum \: of \: n \: terms}}$
• $\leadsto \sf{a = First \: term }$
• $\leadsto \sf{ L = Last \: term}$

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Solution

$: \implies\:{\sf{420 = \dfrac{n}{2} \Big(5 + 30\Big)}}$

$: \implies\:{\sf{420 }}= \sf \dfrac{n}{2}\times 35$

$: \implies\:{\sf{420 }}= \sf \dfrac{35 \: n}{2}$

$: \implies\:{\sf{n }}= \sf \dfrac{420 \times 2}{35}$

$: \implies\:{\sf{n }}= \sf \cancel\dfrac{840}{35}$

$: \implies\sf{n = 24}$

$: \implies \large \underline{\boxed{\sf \purple{n} = \pink{ 24}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore

• ➥ The value of n 24