Question

Find the sum of all number s from 50 to 350 which are divisible by 6 and hence find the 15th term of that arithmetic progression?

Answer 1

hope this helps. the answer is 10050

Answer 2

Answer:

The number of integers between 50 and 350 which are divisible by 6 are 50.

The 15th term of that arithmetic progression is 138.

Step-by-step explanation:

To find : Find the sum of all number s from 50 to 350 which are divisible by 6 and hence find the 15th term of that arithmetic progression?

Solution :

The integers between 50 to 350 which are divisible by 6 are :

 54, 60,66.....348.

This is an AP, the first term is 54 and the last term is 348.

Last term is $L=a+(n-1)d$

where, n is the number of terms , a is the first term and d is the common difference.

a=54 , d=6 , L=348

$348=54+(n-1)6$

$294=(n-1)6$

$n-1=49$

$n=50$

The number of integers between 50 and 350 which are divisible by 6 are 50.

The 15th term of that arithmetic progression,

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

$T_{15}=54+(15-1)6$

$T_{15}=54+(14)6$

$T_{15}=54+(14)6$

$T_{15}=54+84$

$T_{15}=138$

The 15th term of that arithmetic progression is 138.