Question

The first term and last term of an ap as 1 and 11 if the sum of it's term in 36 then the number of term will be

Answer 1

Answer:

The number of terms is  6.

Step-by-step explanation:

First, lets see what we have

First term = 1

Last term = 11

Sum of terms = 36

lets denote first term, last term and sum of terms as a, $a_{n}$ and $S_{n}$ respectively. And n denotes number of terms.

As we know that,

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

by putting the values given, we get

$11 = 1 + (n-1)d \\10=(n-1)d$  . . . . . . . . . . . (1)

Also,

$S_{n} = \frac{n}{2}( {2a+(n-1)d})$

by putting the values of sum of terms and equ(1) we get,

$36 = \frac{n}{2}(2(1) + 10)\\ 36 = \frac{n}{2}(12)\\ 36 = 6n\\n= 6$

hence the number of terms is 6

hope it helps

jerri