Question

Two APs have the same common difference. The first
term of one of these is 3 and that of the other is 8.
What is the difference between their
(1) 2nd terms?
(ii) 20th terms?​

Answer 1

AnswEr :

Remeber – To Calculate the nth term of an AP formula is Given by » aₙ = a + (n – 1)d «

where,

• a = First Term
• n = n term
• d = Common difference

Let the Common difference of the AP be d. We're provided with First Term of Both AP's 3 and 8. We're asked to find out the difference b/w their 2nd and 20th term.

⠀

$:\implies\sf a_n = \Big[3 + (n - 1)d\Big] \;and, \;b_n = \Big[8 + (n - 1)d\Big]$

$:\implies\sf a_n - b_n = \Big[3 + (n - 1)d\Big] - \Big[8 + (n - 1)d\Big]$

$:\implies\sf a_n - b_n = 3 + \cancel{(n - 1)d} - 8 - \cancel{(n - 1)d}$

$:\implies\sf a_n - b_n = 3 - 8$

$:\implies{\pmb{\bf{ a_n - b_n = - 5}}}$

$\therefore$ Hence, Difference b/w their 2nd and 20th term is – 5.

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Answer 2

Given :-

Two Ps have the same common difference. The first

term of one of these is 3 and that of the other is 8.

To Find :-

What is the difference between their

(1) 2nd terms?

(ii) 20th terms?​

Solution :-

We know that

aₙ = a + (n - 1)d

For AP 1

a₁ = 3 + (n - 1)d

a₁ = 3 + d(n - 1)

For AP 2

a₁ = 8 + (n - 1)d

a₁ = 8 + d(n - 1)

Finding difference

3 + d(n - 1) - [8 + d(n - 1)

3 + d(n - 1) - 8 - d(n - 1)

3 + n - 1 - 8 - n + 1

3 - 8

-5

Therefore

The difference between their 2nd and 20th term is -5