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In an AP, Given a =5, d = 3, a_n = 50, find n and S_n.

Question

In an AP,
Given $a = 5, d = 3,$ $a_{n}$ $= 50$ , find $n$ and $S_{n}$ .

330

390

440

560

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Luna Discussed

In an AP,
Given

a = 5, d = 3,

a_{n}

= 50

, find

n

and

S_{n}

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

As we know nth term,

a_{n} = a + (n - 1) d

& Sum of first

n

terms,

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

, where

a

d

are the first term amd common difference of an AP.

Given,

a = 5, d = 3, a_{n} = 50

\Rightarrow a + (n - 1) d = 50

\Rightarrow 5 + (n - 1) 3 = 50

\Rightarrow 5 + 3 n - 3 = 50 \Rightarrow 3 n = 48 \Rightarrow n = 16

∴ S_{16} = \frac{16}{2} [2 a + (16 - 1) d] = 8 [2 \times 5 + 15 \times 3] = 440

Hence,

n = 16, S_{16} = 440

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Question Text	In an AP, Given $a = 5, d = 3,$ $a_{n}$ $= 50$ , find $n$ and $S_{n}$ .
Answer Type	Text solution:1
Upvotes	150