Which term of the series 12+9+6+.......is equal to-100
Answers
Step-by-step explanation:
-100 is not a term of the series.........
No - 100 is not a term of the series
Given :
The series 12 + 9 + 6 + . . . . .
To find :
Which term of the series is - 100
Concept :
The nth term of an AP is
aₙ = a + (n - 1 )d.
a = first term
aₙ = nth term
d = common difference.
Solution :
Step 1 of 3 :
Write down the given series
Here the given series is 12 + 9 + 6 + . . . . .
This is an arithmetic series
Step 2 of 3 :
Write down first term and common difference
First term = a = 12
Common Difference = d = 9 - 12 = - 3
Step 3 of 3 :
Find which term of the series is - 100
If possible let - 100 is nth term of the series
Then nth term of the series = - 100
a + (n - 1 l)d = - 100
⇒ 12 + (n - 1) × ( - 3 ) = - 100
⇒ 12 - 3n + 3 = - 100
⇒ - 3n + 15 = - 100
⇒ - 3n = - 115
⇒ n = 115/3
Now 115/3 is not a natural number
Hence - 100 can not be a term of the series 12 + 9 + 6 + . . . . .
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