Question

2.
For an A.P., the first term is 4 and the last term is 31. The sum of all the terms is
420. What is the value of n?
(a)
12
(b) 24
(c) 10
(d) 20​

Answer 1

Given that,

• The first term of an Arithmetic Progression (AP) is 4. And, the last term is 31.

☯ Let the first term be a.

And, Last term be l.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• The sum of all the terms is 420.

⠀⠀⠀

⠀⠀⠀$\dag\;{\underline{\frak{By \ using \:Formula,}}}$⠀⠀

⠀⠀⠀

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

⠀⠀⠀

$:\implies\sf 420 = \dfrac{n}{2} \Big(4 + 31 \Big) \\\\\\:\implies\sf 420 = \dfrac{n}{2} \Big(35 \Big) \\\\\\:\implies\sf \dfrac{n}{2} = 12 \\\\\\:\implies{\underline{\boxed{\frak{\purple{n = 24}}}}} \: \bigstar$

⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\ The \ value \ of \ 'n' \:is\: {\textsf{\textbf{ Option (b) 24}}}.}}}$

Answer 2

Given that,

The first term of an Arithmetic Progression (AP) is 4. And, the last term is 31.

☯ Let the first term be a.

And, Last term be l.

The sum of all the terms is 420.

⠀...By usingFormula

:⟹ 420= n/2 (4+31)

:⟹ 420 = n/2 (35)

:⟹ n/2 = 12

:⟹ n = 24

hence your correct answer is (b) 24...

mark be brainliest please and verified this answer...