Question

What is the sum of 2n-1 from 1-19 in geometric sequence?

Answer 1

For the given sequence 2n-1,

Let n=1 , so the first term of the sequence = $(2 \times 1) -1 =1$

For n=2, the second term of the sequence= $(2 \times 2) -1 =3$

For n =3, the third term of the sequence = $=(2 \times 3) -1 =5$

Similarly, for n= 19, the last term of the sequence = $(2 \times 19) -1 =37$

Therefore, the sequence is $1,3,5,7,....37$

Since the common difference of the sequence formed is 2 which is same throughout the sequence. Hence, it forms an arithmetic progression.

Sum of arithmetic progression is given by = $\frac{n}{2}(a+l)$

where 'a' is the first term and 'l' is the last term of the given sequence.

Sum= $\frac{19}{2}(1+37)$

=$361$