arithmetic sequence

Question

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

a₁=15 and a₁₀₀=307

Answer 1

There's a formula for the sum of the first n terms of an arithmetic sequence. You should look it up in your textbook (or other learning material). It's

S_n = (n/2)(a₁ + a_n)

Just plug in the numbers and do the arithmetic.

For example, if you wanted to find the sum of the first 10 terms of an arithmetic sequence with a₁ = 40 and common difference d = -3, you would first find a₁₀ = a₁ + (10-1)*(-3) = 40 - 27 = 13, and then find

S₁₀ = (10/2)(40 + 13) = 265