Question

For an A.P., if t1 = 4, tn = 28, Sn= 64, find n.​

Answer 1

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Answer 2

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.