Question

A,a+d,a+2d...l are n terms of an ap,find [n-1]th term of it in terms of l. by brainly

Answer 1

L=a+(n-1)d ie a= L-(n-1)d
(n-1)th term = a+(n-2)d
                   = L-(n-1)d + (n-2)d
                   = L -dn +d +dn -2d
                   = L-d, final answer

Answer 2

A.P. = a , a+d , a+2d ................ a + (n-1) d

Sn = a + a +d + a+ 2d + ................ + a+ (n-1) d ----------------- (1)

On reversing the order of the given A.P. we get,

Sn = a + (n-1) d + a + (n-2) d + .............. + a +d + a ----------------- (2)

Adding the corresponding terms of eqn (1) & eqn (2) , we get ,

2Sn = { 2a + (n-1) d } + { 2a + (n-1) d } + { 2a + (n-1) d } ............... { 2a + (n-1) d }

2Sn = n { 2a + (n-1) d } ( 2a + (n-1) d has been repeated n times)

Sn = n/2 { 2a + (n-1) d }

Hope This Helps.......