Question

Two AP’S have the same common difference. The difference of their 100th term is 100,what is the difference between their 1000th term is ???
(Step by step,please!)

Answer 1

Answer:

We know that,

aⁿ = a + (n+1) d

so, 100th term will be

a power 100 = a + (100-1)d

a power 100 = a + 99d

so,

100th term of 1st AP = a + 99d

let the second AP be denoted as

bⁿ = b+ (n-1)d

b power 100 = b +(100-1)d

b power 100 = b + 99d

so, the 100th term of 2nd AP = b + 99d

Hope it will be helpful

Answer 2

$\huge{\underline{\bf{\red{Solution:-}}}}$

$:\implies\:T_100-T_100=100$

we know that T100 = a+99d.

So,

$:\implies\:a_1+99d-(a_2+99d)=100$

$:\implies\:a_1 + { \cancel{99d}} -a_2-{\cancel{99d}}=100$

$:\implies\:a_1-a_2=100...........(1)$

$:\implies\:T_1000-T_1000$

We know that T100 = a+999d.

$=a_1+999d-(a_2+999d$

$:\implies\:a_1 + { \cancel{999d}} -a_2-{\cancel{999d}}=100$

$:\implies\:a_1-a_2$

we know that a1- a2=100 from (i)

then ,

$:\implies\:\bf\:T_1000-T_1000=100$

━━━━━━━━━━━━━━━━━━━━━━━━━