UGC NET Paper 1 GA 5 Jan 2022 Shift 2 Paper

Question : 14 of 50

Marks: +1, -0

How many terms are there in the following sequences?
1, 2, 4, 8, ..,...............,., 4096

Solution:

As we know that general Term

( {n}^{\;\text "th "\;}

Term

)=a_{n}=a r^{(n-1)}

Here,

a=1, r=2

and

a_{n}=4096

⇒ {a}_{ {n}}= {ar}^{( {n}-1)}

⇒ 4096=1 × 2^{( {n}-1)}

⇒ 2^{12}=2^{( {n}-1)} \;\; [\;\text " If "\; {a}^{ {m}}= {a}^{ {n}} \;\text " then, "\; {m}= {n}]

⇒ 12= {n}-1

⇒ {n}=13

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