Question

Find the sum of the first 30 terms of the sequence below. an=4n+1

Answer 1

That would be 1,890.

Answer 2

Answer: The sum of first 30 terms of the given sequence is 1890.

Step-by-step explanation: We are given to find the sum of first 30 terms of the following sequence :

`a_n=4n+1.`

The first few terms of the above sequence are

`a_1=5,\\\\a_2=9,\\\\a_3=13,\\\\a_4=17,\\\\a_5=21\\\\\vdots~~~~~\vdots~~~~~\vdots\\\\`

So, the given sequence is an arithmetic one with first term 5 and common difference

d = 9 - 5 = 13 - 9 = 17 - 13 = . . . = 4.

Therefore, the sum of first 30 terms will be

`S_(30)\\\\\\=(30)/(2)\{2a_1+(30-1)d\}\\\\\\=15(2*5+29*4)\\\\=15(10+116)\\\\=15* 126\\\\=1890.`

Thus, the sum of first 30 terms of the given sequence is 1890.