ಒಂದು ಸಮಾಂತರ ಶ್ರೇಢಿಯ 5 ನೇ ಮತ್ತು 10 ನೇ ಪದ
ಗಳ ಅನುಪಾತ 1:2 ಮತ್ತು 12 ನೇ ಪದವು 36 ಆದಾಗ
ಶ್ರೇಢಿಯನ್ನು ಬರೆಯಿರಿ.
Answers
Given :- if the ratio between 5th and the 10th terms of an AP is 1:2 and 12th term is 36,find that AP ?
Answer :-
we know that, nth term of an AP is given by,
- T(n) = a + (n - 1)d where,
- a = first term
- d = common difference .
- n = nth term .
so, let first term of AP is a and common difference is d.
A/q,
→ T(5)/T(10) = 1/2
→ [a + (5 - 1)d] / [a + (10 - 1)d] = 1/2
→ (a + 4d)/(a + 9d) = 1/2
→ 2a + 8d = a + 9d
→ 2a - a = 9d - 8d
→ a = d ------ Eqn.(1)
then,
→ T(12) = a + (12 - 1)d
→ 36 = a + 11d
using Eqn.(1),
→ 36 = a + 11a
→ 12a = 36
→ a = 3 .
therefore,
→ d = a = 3 .
hence,
→ Required AP = a , (a + d) , (a + 2d) , (a + 3d) ________ = 3 , 6 , 9 , 12 , 15, 18 ________ .
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