For an A.P., if t1 = 4, tn = 28, Sn= 64, find n.
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Given,
For an A.P.,
t1 = 4
tn = 28
Sn = 64
To find,
The value of n.
Solution,
The value of n will be 4.
We can easily solve this problem by following the given steps.
According to the question,
For an A.P.,
t1 = 4
tn = 28
Sn = 64
We know that t1 is the first term (also denoted by a), tn is the last term ( also denoted by l), and Sn is the sum of all the terms in a series.
There are two formulas to find the sum of all the terms in an A.P.
Sn = n/2 [2a+(n-1)d]
Sn = n/2 (a+l)
Using the second formula, we can quickly find the value of n.
Sn = n/2 (a+l)
64 = n/2 (4+28)
64 = n/2 (32)
64 = 32n/2
64 = 16n
64/16 = n ( 16 was in the multiplication on the right-hand side. So, it is in the division on the left-hand side.)
4 = n or n = 4
Hence, the value of n for the given series is 4.