Question

The number of terms in the given Ap 13, 17, 21... 293 is equal to

Answer 1

Answer:

a=13

d=17-13=4

an=293

$an = a + (n - 1)d \\ 293 = 13 + (n - 1)4 \\ 293 - 13 = 4n - 4 \\ 280 + 4 = 4n \\ \frac{284}{4} = n \\ 72 = n$

Answer 2

The given question is The number of terms in the given Ap 13, 17, 21... 293 is equal to

The given sequence is 13,17,21,.......293.

we have to find the number of terms there in the sequence.

The Arithmetic progression or sequence is the series of numbers, in which the difference between the consecutive terms is constant.

The first term in the sequence is a = 13.

The common difference d is the second term - first term.

The second term is 17.

d = 17-13=4.

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

an = a+( n-1)d

The nth term is 293.

substitute the values in the above formula, we get the

value as

$293 = 13 + (n - 1)4$

multiply 4 with n-1.

$293 = 13 + 4n - 4 \\ 293 - 13 + 4 = 4n$

$280 + 4 = 284$

$284 = 4n$

$\frac{284}{4} = n \\ n = 71$

Therefore, the number of terms in the given series is 71

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