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If nth term of a G.P. is 2n then find the sum of its first 6 terms.
- a)126
- b)124
- c)190
- d)154
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If nth term of a G.P. is 2n then find the sum of its first 6 terms.a)1...
Concept:
Sum of n terms of a Geometric Progression,
Explanation:
Given that an = 2n of the G.P.
Then, a1 = 2
a2 = 4
a3 = 8
i.e. G.P. series is 2, 4, 8, 16, 32, . . .
where first term, a = 2 ;
Common ration, r = 4/2 = 8/4=...=2 ,
Number of terms, n = 6 (given in the question)
⇒ 2(64 - 1)
⇒ 2(63)
⇒ 126
Sum of n terms of a Geometric Progression,
Explanation:
Given that an = 2n of the G.P.
Then, a1 = 2
a2 = 4
a3 = 8
i.e. G.P. series is 2, 4, 8, 16, 32, . . .
where first term, a = 2 ;
Common ration, r = 4/2 = 8/4=...=2 ,
Number of terms, n = 6 (given in the question)
⇒ 2(64 - 1)
⇒ 2(63)
⇒ 126
Most Upvoted Answer
If nth term of a G.P. is 2n then find the sum of its first 6 terms.a)1...
Given G.P. and nth term
The given G.P. is 2, 4, 8, 16, ...
The nth term of this G.P. is given as 2n.
Finding the common ratio
To find the common ratio of the G.P., we can divide the second term by the first term:
Common ratio (r) = 4/2 = 2
Finding the first term of the G.P.
Since the nth term of the G.P. is 2n, we can substitute n = 1 to find the first term:
First term (a) = 2(1) = 2
Finding the sum of the first 6 terms
The sum of the first n terms of a G.P. is given by the formula:
Sum of n terms = a(r^n - 1) / (r - 1)
Substitute the values into the formula for n = 6:
Sum of first 6 terms = 2(2^6 - 1) / (2 - 1) = 2(64 - 1) / 1 = 2(63) = 126
Therefore, the sum of the first 6 terms of the given G.P. is 126, which corresponds to option 'A'.
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If nth term of a G.P. is 2n then find the sum of its first 6 terms.a)126b)124c)190d)154Correct answer is option 'A'. Can you explain this answer?
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