Answer:
AIRTHMETIC PROGRESSION:
The number of sequence
a
,
a
+
d
,
a
+
2
d
,
a
+
3
d
,
.
.
.
.
.
is known as arithmetic sequence. In this sequence d is the difference between each consecutive term that is constant.
The formula for the nth term of an arithmetic sequence is,
T
n
=
a
+
(
n
−
1
)
d
The formula for the sum of first n terms of the sequence is,
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
Answer and Explanation:
Become a Study.com member to unlock this answer! Create your account
Given data:
{eq}\begin{align*} {a_1} = 1,{a_2} = 2,{b_1} = 0,{b_2} = 1\\ n \ge 3\,;\,{a_n} &= 2{a_{n - 1}} + {b_{n - 1}}\\ n \ge 2\,;\,{b_n} &=...
Answer:
1, 5, 17, 53, 161
Step-by-step explanation:
Using the recursive rule and a₁ = 1 , then
a₂ = 3a₁ + 2 = 3(1) + 2 = 3 + 2 = 5
a₃ = 3a₂ + 2 = 3(5) + 2 = 15 + 2 = 17
a₄ = 3a₃ + 2 = 3(17) + 2 = 51 + 2 = 53
a₅ = 3a₄ + 2 = 3(53) + 2 = 159 + 2 = 161
The first 5 terms are 1, 5, 17, 53, 161
