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Formula for Sum of n Terms of an AP

Given a=8, ...

Question

Given $a = 8, a_{n} = 62, S_{n} = 210$ , find n and d

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Solution

$S_{n} = 210 = \frac{n}{2} (8 + 62)$
$\Rightarrow 35 n = 210$
$\Rightarrow n = 210 \div 35 = 6$
Now, $62 = 8 + 5 d$
$\Rightarrow 5 d = 62 - 8 = 54$
$\Rightarrow d = 54 \div 5 = 10.8$

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Similar questions

In an AP given a=8,a_n=62,S_n=210,find n and d.

Find n and d where a=8 , a_n=62 ,S_n=210.

Q. Question 3 (vii)
In an AP:
(vii) Given a = 8,

a_{n} = 62

S_{n} = 210

, find n and d.

Q. In an AP:
(i) Given

a = 5, d = 3

a_{n} = 50

n

S_{n}

a = 7

a_{13} = 35

d

S_{13}

a_{12} = 37

d = 3

a

S_{12}

a_{3} = 15

S_{10} = 125

d

a_{10}

d = 5

S_{9} = 75

a

a_{9}

a = 2, d = 8

S_{n} = 90

n

a_{n}

a = 8

a_{n} = 62

S_{n} = 210

n

d

a_{n} = 4

d = 2

S_{n} = - 14

n

a

a = 3, n = 8, S = 192

d

l = 28, S = 144

, and there are total 9 terms. Find

a

In an AP

(i) Given $a = 5, d = 3, a_{n} = 50$ , find $n$ and $S_{n}$ .

(ii) Given $a = 7, a_{13} = 35$ , find $d$ and $S_{13}$ .

(iii) Given $a_{12} = 37, d = 3$ , find $a$ and $S_{12}$ .

(iv) Given $a_{3} = 15, S_{10} = 125$ , find $d$ and $a_{10}$ .

(v) Given $d = 5, S_{9} = 75$ , find $a$ and $a_{9}$ .

(vi) Given $a = 2, d = 8, S_{n} = 90$ , find $n$ and $a_{n}$ .

(vii) Given $a = 8, a_{n} = 62, S_{n} = 210$ , find $n$ and $d$ .

(viii) Given $a_{n} = 4, d = 2, S_{n} = - 14$ , find $n$ and $a$ .

(ix) Given $a = 3, n = 8, S_{8} = 192$ , find $d$ .

(x) Given $l = 28, S_{n} = 144$ and there are total $9$ terms. Find $a$ .

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