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The sum of first 16 terms of the A.P. 10,6,2,... is
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Solution
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Correct option is A)
Hint:- The sum formula for n terms of an A.P. (
2
n
{2a+(n−1)d}) will be used along with the related terms.
Given:-
Sequence: 10,6,2,...
a=10=first term
n=16=no. of terms
Step 1: Finding the common difference 'd' of the given sequence 10,6,2,....
second term − first term =a
2
−a
1
=6−10=−4
third term − second term =a
3
−a
2
=2−6=−4
As the difference is same in all the cases, hence it's common difference=d=−4
Step 2: Finding the sum of the first 16 terms by replacing the given terms in the sum formula of A.P.
S
n
=
2
n
{2a+(n−1)d}
So replacing the required terms in the formula we will get,
S
16
=
2
16
{2×10+(16−1)d}
=
2
16
{20+15×(−4)}
=
2
16
(20−60)
=8(−40)
=8×(−40)
=−320
Hence, the sum of the first 16 terms would be −320
Final Step: Hence, the sum of the first 16 terms would be −320
Step-by-step explanation:
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Step-by-step explanation:
In ques 1 for finding discriminant of the eq use D= b square - 4 ac and with this only u can also find the nature of roots by the value of d , is greater or smaller or equal ....
In ques 2 for finding 16th term use the formula An= a + ( n - 1 ) * d...with this you will get your 16th term...
hope it helped ...✌️