Question

the second term and sixth term of an AP are 6 and 18 respectively find its first term and common difference describe this question solution​

Answer 1

Let a be the first term and d be the common difference.

Then,by question, we get

second term=6

or a+d=6--------(i)

Now, sixth term =18

or a+5d=18---------(ii)

subtracting (i) from (ii),we get

a+5d-a-d=18-6

or 4d=12

or d=3

Using the value of d in equation (i),we get

a+3=6

or a=3

Therefore the first term and common difference of the A.P are respectively 3 and 3.

In this calculation I used the formula "Nth term of a=a+(n-1)d".

Hope this will help you.

Answer 2

$second \: term \: (a) = 6 \\ \\ = > a + d = 6 - eq(1) \\ \\ sixth \: term \: = 18 \\ \\ = > a + 5d = 18 -eq(2) \\ \\ subtracting \: eq(1) \: and \: eq(2) \\ \\ \: \: \: \: \: a + 5d = 18 \\ \\ \: \: \: \: \: a + d = 6 \\ ( - ) \: \: ( - ) \: \: ( - ) \\ \\ - - - - - - - - \\ \\ = > 4d = 12 = > d = 3 \\ \\ from \: eq(1) \\ \\ a = 6 - d = 6 - 3 = 3$

∴ THE FIRST TERM (a) = 3 & COMMON

DIFFERENCE(d) = 3