Step-by-step explanation:
1) The first term is -1352, and the common difference is 18. So the 87th term is:
a = -1352 + 18 (87 − 1)
a = 196
2) 1/64 + 1/16 + 1/4 + 1 + 4
This is a geometric series, where the first term is 1/64 and the common ratio is 4.
∑⁵ᵢ₌₁ 1/64 (4)ⁱ⁻¹
Since 1/64 = 4⁻³:
∑⁵ᵢ₌₁ 4⁻³ (4)ⁱ⁻¹
∑⁵ᵢ₌₁ (4)ⁱ⁻⁴
3) The first term is -2100, and the common ratio is -0.1, so the 7th term is:
a = -2100 (-0.1)⁷⁻¹
a = -0.0021
4) The first term is 48, and the fifth term is 243/16, so the common ratio is:
243/16 = 48 r⁵⁻¹
81/256 = r⁴
r = 3/4
So the sequence is:
48, 36, 27, 81/4, 243/16
