Question

Find the common difference and the SIMPLIFIED general term formula.

3) a 14=1322 and a 38 = 3722

I reallyyyy need help!!! ASAP PLEASE!!!!!

Answer 1

`a_(n)` = 100n - 78

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₁₄ = 1322 and a₃₈ = 3722 , then

a₁ + 13d = 1322 → (1)

a₁ + 37d = 3722 → (2)

subtract (1) from (2) term by term to eliminate a₁

24d = 2400 ( divide both sides by 24 )

d = 100

substitute d = 100 into either of the 2 equations and solve for a₁

substituting into (1)

a₁ + 13(100) = 1322

a₁ + 1300 = 1322 ( subtract 1300 from both sides )

a₁ = 22

then nth term formula is

`a_(n)` = 22 + 100(n - 1) = 22 + 100n - 100 = 100n - 78