Question

Two arithmetic progressions has the same common difference. If the first term

of the first progression is 3 and that of the other is 8, then the difference between

their 3rd term is

A. 2
B. 3

C. 4
D. 5​

Answer 1

Answer:

d.5

Step-by-step explanation:

$\color{orange} \boxed{ \color{blue}\boxed{ \mathbb{ \colorbox{red}{ \color{yellow}Given :-}}}}$

$: \implies \: first \: term \: of \: the \: first \: AP, a= 3$

$: \implies first \: term \: of \: second \: AP , a' = 8$

Now, term of first AP

$\implies \: a_3 = 3 + (3 - 1)d$

$\implies \: a_3 = 3 + 2d$

Third term of second AP,

$a'_3 = 8 + (3 - 1)d$

$a'_3 = 8 + 2d$

According to the question, difference of their third term

$\implies \: a'_3 - a_3$

$\implies \: (8 + 2d) - (3 + 2d)$

$\implies \: 8 + 2d - 3 - 2d$

$\implies \: \boxed{ 5}$

Hence the difference between their third terms is 5, and option d is correct one