Question

Q4 : Two APs have the same common difference, 1st t2rm of one is 3 and that of other is 8, the difference between their 2nd terms is



-3

-5

-10

-4

​

Answer 1

${\underline{\sf{Question}}}$

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 2nd terms?

${\underline{\sf{Theory}}}$

General term of an AP is given by :

$\bf \: a_{n} = a + (n - 1)d$

where

a = first term

d = common difference

n = no of terms

${\underline{\sf{Solution}}}$

Let the common differnce of both the Ap.s be d .

First Ap:

First term = a = 3

common difference = d

$\sf \:\implies\:a_{n} = 3+ (n - 1)d$

$\sf \:\implies\:a_{n} = 3 + nd-d$

Second Ap:

First term = a = 8

common difference = d

$\sf \:\implies b_{n} = 8+ (n - 1)d$

$\sf \:\implies\:b_{n} =8+ nd-d$

⇒Difference between 2nd term

$\sf \:= a_{n}-b_{n}$

$\sf \:=(3+nd-d)-(8+nd-d)$

$\sf \: = 3-8$

$\sf \:= -5$

Therefore , difference between their 2nd terms is -5.

Answer 2

Answer:

⠀⠀⋆ Common Difference = d

⠀⠀⋆ First Term of 1st AP = 3

⠀⠀⋆ First Term of 2nd AP = 8

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf Difference=Second\:Term_{(First\:AP-Second\:AP)}\\\\\\:\implies\sf Difference=\bigg\lgroup a_1+(n-1)d\bigg\rgroup-\bigg\lgroup a_2+(n-1)d\bigg\rgroup\\\\\\:\implies\sf Difference=\bigg\lgroup3-(2-1)d\bigg\rgroup-\bigg\lgroup8-(2-1)d\bigg\rgroup\\\\\\:\implies\sf Difference=\bigg\lgroup3-d\bigg\rgroup-\bigg\lgroup8-d\bigg\rgroup\\\\\\:\implies\sf Difference=3-d-8+d\\\\\\:\implies\sf Difference=3-8\\\\\\:\implies\underline{\boxed{\sf Difference=-\:5}}$

⠀

$\therefore\:\underline{\textsf{Difference b/w their 2nd terms is b) \textbf{- 5}}}.$