Question

the numbers of terms in the series 101 + 99 + 97 + - - - + 47 is​

Answer 1

Answer:

Step-by-step explanation:Here The first term, a = 101

common difference, d = 99 - 101= -2

Last term =47

Let the number of terms be n

Then,

47=101+(n-1) *(-2)

=101-2n+2

=103-2n

or, 2n=103-47

or, n = 56/2=28

No. of terms = 28.

Answer 2

The given question is we have to find the number of terms in the series.

The given series is 101 + 99 + 97 + - - - + 47 is

The first term in the series is 101.

The last term in the series is 47.

We have to find the total number of terms in the series.

The formula to find the total number of terms in the series is

an= a+(n-1)d.

where a is the first term and d is a common difference.

The value of a is 101.

The common difference is obtained by subtracting the first term from the second term.

d = t2 - t1.

d= 99-101= -2.

a = 101

let us substitute the values in the formula we get,

$an \: = a + (n - 1)d$

$47= 101 + (n - 1)( - 2)$

let's proceed the further calculation, we get

$101 + ( - 2n) + 2 = 47\\ 103 - 2n =47 \\ 103-47 = 2n$

56=2n.

The value of n is 56/2= 28.

The value of n is 28.

Therefore, the number of terms in the series is 28.

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