Question

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

Answer 1

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

$S_{30}\\\\\\=\dfrac{30}{2}\{2a_1+(30-1)d\}\\\\\\=15(2\times5+29\times4)\\\\=15(10+116)\\\\=15\times 126\\\\=1890.$

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

Answer 2

That would be 1,890.