or an an arithmetic sequence ag 10 and a22 3 Find the first

or an an arithmetic sequence ag 10 and a22 3. Find the first term, the common difference and simplified

Solution

a8 = 10 ; a22 = 3

nth term of A.P. : an = a1 +(n-1)d

10 = a1 + (8-1)d

10 = a1 +7d ---(1)

3 = a1 +( 22-1)d

3 = a1 +21d ---(2)

from 1 and 2 we get : -7 = 14d

d= -1/2

a1 = 10 -7d = 10 - 7(-1/2) = 10 +7/2 = 27/2