Answer:
The original sequence we wanted: 7, 11, 15, 19, 23, ... ... Hence, the general formula for the nth term of the original sequence is 4n + 3.
Step by Step Explanation:
Arithmetic Sequnce
To find the common difference, we may use the formula:
d = \frac{a_k - a_m}{k - m}
k−mak −am
(in whick 'k' is the higher term)
d = \frac{7 - 3}{2 - 1}
2−1
7−3
d = \frac{4}{1}
1
4
d = 4
Substitute the given values in the formula:
a_{n}a
n
= a_{1}a
1
+ (n-1) d
a_{n}a
n
= 3 + (n-1) 4
a_{n}a
n
= 3 + (4n-4)
a_{n}a
n
= 3 + 4n - 4
a_{n}a
n
= 4n - 1
Proving:
a_{n}a
n
= 4n - 1
a_{2}a
2
= 4(2) - 1
a_{2}a
2
= 8 - 1
a_{2}a
2
= 7 ✔
Thus, the nth term is equal to 4n - 1
Hope it helps!
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