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Find the 12^{th} term from the end of the following arithmetic

Question

Find the $1 2^{th}$ term from the end of the following arithmetic progressions:
(i) $3, 5, 7, 9, .......201$
(ii) $3, 8, 13, .........253$
(iii) $1, 4, 7, 10, ......88$

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Liam Discussed

Find the

1 2^{th}

term from the end of the following arithmetic progressions:
(i)

3, 5, 7, 9, .......201

(ii)

3, 8, 13, .........253

(iii)

1, 4, 7, 10, ......88

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Text solutionVerified

(i)

a = 201

d = - 3 + 5 = + 2

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

201 = 3 + (n - 1) 2

99 = n - 1

n = 100

12 t h

sum from end

\Rightarrow a + 88 d = 3 + 88 \times 2 = 3 + 176 = 179

(ii)

3, 8, 18.................253

a = 3

d = 5

253 = 3 + (n - 1) 5

\frac{250}{5}

n - 1 \Rightarrow n = 51

12 t h

term from the end

\Rightarrow

a + 39 d

3 + 39 \times 5 = 3 + 195 = 198

(iii)

1, 4, 7, 10............88

a = 1

d = 3

88 = a + (n - 1) d = 1 + (n - 1) 3

n = \frac{87}{3} = 29

12 t h

sum from the end

= a + 17 d

= 1 + 17 \times 3 = 52

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Question Text	Find the $1 2^{th}$ term from the end of the following arithmetic progressions: (i) $3, 5, 7, 9, .......201$ (ii) $3, 8, 13, .........253$ (iii) $1, 4, 7, 10, ......88$
Answer Type	Text solution:1
Upvotes	150