there are 25terms in a progression. Addition of first and last term is equal to multiple of of 25 terms. Calculate the sum of the 25 terms
Answers
Answer:
None of these
Given, T
n
=7−3n.
Let us try to reaarange it into the form, T
n
=a+(n−1)d
where a is the first term,n is the number of terms and d is the common difference.
T
n
=7−3n
⇒ T
n
=4+3−3n
⇒ T
n
=4−3(n−1)
So,here a=4,d=−3
Sum of n terms in an AP can be calculated using the formula
S
n
=
2
n
(a+T
n
)
⇒ S
n
=
2
n
(4+7−3n)
⇒ S
n
=
2
n
(11−3n)
⇒ S
n
=
2
25
(−64) (∵n=25)
⇒ S
n
=−800
∴ No Option
Answer:
Question:-
Sum of first 25 term of A.P. is 250.find middle term i.e. 13th term.
___________________________
Required Answer:-
Given:- S25=250
To Find:- t13=?
Solution:-
S25=250
Formula:- Sn=n/2x[2a+(n-1)d]
Sn=n/2[2a+(n-1)d]
S25=25/2[2a+(25-1)d]
250=25/2[2a+24d]
250x2=25x2[a+12d]
500=50[a+12d]
500/50=a+12d
10=a+12d -(i)
__________________________
t13=?
Formula:- tn=a+(n-1)d
tn=a+(n-1)d
t13=a+(13-1)d
t13=a+12d -(ii)
From (i) and (ii),
t13=10 -[Both RHS of (i) and (ii) are equal]
________________________
Hope it help you :)