Question

Di gai samantar shreni ka chhatha pad gyat kijiye. 17,11,14.................


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Answer 1

दी गई समान्तर श्रेणी का छटा पद ज्ञात कीजिए। 17, 14, 11, ....

दी गई समान्तर श्रेणी:

17, 14, 11, ....

यहाँ, पहले पद (a = $a_{1}$) = 17,  दूसरा पद($a_{2}$) = 14

∴ आम अंतर (d) =   दूसरा पद($a_{2}$) - पहले पद (a = $a_{1}$) = 14 - 17 = - 3

दी गई समान्तर श्रेणी का छटा पद ज्ञात कीजिए।

Solution:

हम जानते हैं कि:

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

∴ समान्तर श्रेणी का छटा पद

$a_{6}$ = 17 + (6 -1)(-3)

⇒ $a_{6}$ = 17 + (5)(-3)

⇒ $a_{6}$ = 17 - 15

⇒ $a_{6}$ = 2

∴ छटा पद ( $a_{6}$) = 2

इसलिये, दी गई समान्तर श्रेणी का छटा पद ( $a_{6}$) 2 होगा।

Answer 2

Given : An AP 17 , 11 , 14 _____________

To Find : Sixth number of series

Solution:

an AP is of of

for a , a + d , a + 2d

Where a = first term of AP

d - common difference of AP

aₙ = a + (n - 1)d   aₙ = nth term

a₆ = a + (6 -1 ) d = a + 5d

17 , 11 , 14 can not be an AP

AP can be 17 , 14 , 11 ________

or

11 , 14 , 17 _________

if AP is 17 , 14 , 11 ________

a = 17

d = - 3

6th term  = a + 5d

= 17 + 5(-3)

= 2

if AP is  11 , 14 , 17 _________

a = 11

d =   3

6th term  = a + 5d

= 11 + 5( 3)

= 26

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