Question

समांतर श्रेणी का चौथा पद शून्य है सिद्ध कीजिए की समांतर श्रेणी का 25 वां पद 11वीं पद का 3 गुना होगा

Answer 1

Answer:

sqmantar shranee me 5 ka pad branpey daiga yani 50

Answer 2

The value of $a_{25}=21d$ which is 3 times of $a_{11}=7d$ proved.

Step-by-step explanation:

Consider the provided information.

The nth term of an AP can be found using the formula: $a_n=a+(n-1)d$

4th term of an AP is 0.

$0=a+(4-1)d$

$a+3d=0$ ......(1)

Now find the 11th term of the AP.

$a_{11}=a+(11-1)d\\\\a_{11}=a+10d\\\\a_{11}=a+3d+7d$

From equation 1.

$a_{11}=0+7d\\\\a_{11}=7d$

Find the 25th term of the AP

$a_{25}=a+(25-1)d\\\\a_{25}=a+24d\\\\a_{25}=a+3d+21d$

From equation 1.

$a_{25}=0+24d\\\\a_{25}=21d$

Now observe that $a_{25}=21d$ which is 3 times of $a_{11}=7d$.

Hence, proved

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