Question

How many terms are there in an A.P. of even numbers 2,4,6,8...,100?​

Answer 1

Answer:

there are 50 numbers in the given a.p.

Step-by-step explanation:

a1=2

a2=4

d=a2-a1=4-2=2

an=100

an=a1+(n-1)d

100=2+(n-1)2

n=50

Answer 2

Step-by-step explanation:

first term of series is a = 2

Last term l = 100

common difference d = 4 - 2 = 2

let number of term in series is n

then from formula

$l = a + (n - 1)d$

$100 = 2 + (n - 1) \times 2$

$100 - 2 = (n - 1) \times 2$

$98 = (n - 1) \times 2$

$\frac{98}{2} = n - 1$

$49 = n - 1$

$n = 49 + 1 = 50$

number of term is= 50

Short method:

If last term is P

then

number of term in first even/odd terms = P/2

then

n = 100/ 2

n = 50

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