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Sum of First N Natural Numbers

Question 3 vI...

Question

Question 3 (v)
In an AP:
(v) Given d = 5, $S_{9} = 75$ , find d and $a_{9}$ .

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Solution

$G i v e n t h a t, d = 5, S_{9} = 75 A s S_{n} = \frac{n}{2} [2 a + (n - 1) d] S_{9} = \frac{9}{2} [2 a + (9 - 1) 5] 25 = \frac{3}{2} (2 a + 40) 25 = 3 a + 60 a = \frac{- 35}{3} a_{n} = a + (n - 1) d, a_{9} = a + (9 - 1) (5) = \frac{- 35}{3} + 8 (5) = \frac{- 35}{3} + 40 = (\frac{- 35 + 120}{3}) = \frac{85}{3}$

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Similar questions

Q. Question 3 (v)
In an AP:
(v) Given d = 5,

S_{9} = 75

a_{9}

Q. In an AP, given d

= 5

S_{9} = 75

a_{9}

Q. In an A.P
i) Given

a = 2, d = 8, S n = 90

a_{9}

d = 5, S_{9} = 75

a & a_{9}

a = 7, a_{13} = 35

d & S_{13}

d = 5, S_{9} = 75

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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Sum of First N Natural Numbers

Standard X Mathematics

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