Question

In an A.P prove that a10=a6+4d

Answer 1

Answer:

a10 = a+ 9d

a6 = a+ 5d

a6 +4d = a+5d +4d = a+ 9d

proved

Answer 2

Answer:

$\large \text{ a_{10}=a_6+4d Proved}$

Step-by-step explanation:

We have to $\large a_{10}=a_6+4d$

We know formula for terms

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

where a = first term

n = numbers of term

d = common difference

when n = 10

$\large a_{10}=a+(10-1)d\\\\\\\large a_{10}=a+9d$

when n= 6

$\large a_{6}=a+(6-1)d\\\\\\\large a_{6}=a+5d$

Now

$\large a_{10}=a_6+4d\\\\\\\large a+9d=a+5d+4d\\\\\\\large a+9d=a+9d$

L.H.S. = R..H.S.

Hence proved.

Thus we get answer.