Question

Find the sum of all numbers from 50 to 350 which are divisible by 4. Also find 15th term.

Answer 1

15th term is 108 and number of terms is 75 above your full solution

Answer 2

Answer: The sum of all numbers is 18260.

Step-by-step explanation:

Since we have given that

Sum of all number from 50 to 350 which are divisible by 4.

So, our sequence becomes,

$56,60,64,.................348$

Here, a = first term = 56

Last term = $a_n=384$

d = common difference = 60-56=4

First we find out the number of terms:

$a_n=a+(n-1)d\\\\384=56+(n-1)4\\\\384-56=4(n-1)\\\\328=4(n-1)\\\\\frac{328}{4}=n-1\\\\82=n-1\\\\82+1=n\\\\n=83$

Now, Sum of all numbers from 50 to 350 which are divisible by 4 is given by

$S_{83}=\frac{n}{2}(2a+(n-1)d)\\\\=\frac{83}{2}(2\times 56+(83-1)4)\\\\=41.5(112+82\times 4)\\\\=41.5\times 440\\\\=18260$

Hence, the sum of all numbers is 18260.