Question

if tn is the nth term of an a.p then t2n - tn is _______​

Answer 1

Answer:

If tn is the nth term of an a.p then t2n - tn is

= n × Common difference

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Answer 2

Answer:

$t_n$ = nd

Step-by-step explanation:

Given,

nth term of an AP is $t_n$

Required to find,

$t_{2n} - tn$

Recall the formula

The nth term of an AP = a+(n-1)d, where 'a' is the first term and 'd' is the common difference

Solution:

We have,

$t_n$ = a + (n-1)d

substituting the value of 'n' as '2n' we get

$t_{2n}$ = a+(2n -1)d

$t_{2n}$ - $t_n$  = a+(2n-1)d - a+(n-1)d

= a+2nd -d -(a+nd -d)

= a+2nd -d -a -nd +d

= 2nd -nd

= nd

∴ $t_{2n}$ - $t_n$ = nd

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