Question

Which term of AP: 21,42,63,84,.......is 210​

Answer 1

Step-by-step explanation:

Given AP : 21 , 42 , 63 , 84 , ...

Here a = 21 and d = 21

Let tn term be 210.

We know that

tn = a + (n - 1)d

210 = 21 + 21n - 21

21n = 210

n = 10

So 210 is the 10th term of the given AP.

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Answer 2

Solution:-

Given:-

$\rm \: first \: term \: (a) = 21$

$\rm \: common \: difference \: (d) = t_2 - t_1 = 42 - 21 = 21$

$\rm \: T_n = 210$

To find

$\rm \: no. \: of \: terms(n)$

formula

$\boxed{ \rm {\: T_n = a + (n - 1)d}}$

Now put the value on formula we get

$\rm \: 210 = 21 + (n - 1)21$

$\rm \: 210 = 21 \{1 + (n - 1) \}$

$\rm \frac{210}{21} = 1 + (n - 1)$

$\rm \: 10 = n$

So number of term is 10

About Arithmetic progression

Arithmetic Progression or an Arithmetic Sequence is a sequence in which a constant is added to each term to get next term in the sequence. The constant term is called as the common difference of the A.P.

Suppose, a1,a2,a3,………an are the terms of an A.P.

Then,a2 = a1+d, a3 = a2+d , where a1 is the 1st term & d is the common difference which is constant for an Arithmetic Progression

In general,an+1 = an+d , where n is any natural number.