find first 4 terms of following sequence:
a1=-6 abd an=2an-1+3 for n >2
To find the first four terms of the sequence, we can substitute the given formula for the n-th term of the sequence and calculate the values step by step.
Given formula: aₙ = 2aₙ₋₁ + 3
Step 1: Finding the first term (a₁)
Since a₁ = -6 is given, we don't need to calculate it.
Step 2: Finding the second term (a₂)
Using the formula, we substitute n = 2 to get:
a₂ = 2a₁ + 3
a₂ = 2(-6) + 3
a₂ = -12 + 3
a₂ = -9
Step 3: Finding the third term (a₃)
Using the formula, we substitute n = 3 to get:
a₃ = 2a₂ + 3
a₃ = 2(-9) + 3
a₃ = -18 + 3
a₃ = -15
Step 4: Finding the fourth term (a₄)
Using the formula, we substitute n = 4 to get:
a₄ = 2a₃ + 3
a₄ = 2(-15) + 3
a₄ = -30 + 3
a₄ = -27
Therefore, the first four terms of the given sequence are:
a₁ = -6, a₂ = -9, a₃ = -15, a₄ = -27.