Find the sum of the first 100 terms of the arithmetic sequence

Question

a1=15 and a100=307, answer is a whole number and if steps were provided it would be helpful, having difficulty understanding

Answer 1

sum of 1st n numbers of an arithmetic sequence is:

n * (a1 + an)/2

so for our problem with n = 100, a1 = 15 and a100 = 307:

sum = 100 * (a1 + a100)/2 = 100 * (15 + 307)/2 = 16,100

Answer 2

There is a formula for the sum of the first n terms of an arithmetic sequence:

S_n = n(a₁+a_n)/2

For this case

S₁₀₀ = 100(15+307)/2 = 50(322) = 16100

Answer 3

a1 = 15

a100= 307

a1 + a100 = 322

a2+a99 = 322

...

a50 + a51 = 322

S100 = 50(322) = 16,100

each pair, of last & first sum to 322

same with 2nd to last and 2nd to first, etc. all summing to 322

there are 50 such pairs, so sum of all = 50 times 322

Answer 4

S₁₀₀ = 100/2(a₁ + a₁₀₀) = 50(15 + 307) = 16100