Question

The common difference of an AP whose 8th term from the last is 30 and last term is 65, is

Answer 1

Answer:

Hope this helps........

Step-by-step explanation:

Answer 2

Answer:

Required Common difference is 5.

Step-by-step explanation:

Let the number of terms be n.

8 th term from last is (n-7)

i.e $a + (n - 7 - 1)d = 30$

last term ,$a + (n - 1)d = 65$

Now $a + (n - 8)d = 30......(1)$

and $a + (n - 1)d = 65.....(2)$

Subtracting equation (2) from equation (1),

$(n - 1)d - (n - 8)d = 65 - 30$

$d(n - 1 - n - 8) = 35$

$d \times 7 = 35 \\ d = \frac{35}{7} = 5$

The common difference is 5.

Some formulas of AP series are

$a_n=a_1+(n-1)d \\ S_n= \frac{n}{2} [2a+(n-1)d] \\ d=a_n -a_n-1 \\ S_n= \frac{n}{2} [a_1+a_n]$