What is the general term of the arithmetic sequence – 32, – 25, –18, –11, …?

$3355

Step-by-step explanation:

Since the job offers starting salary of $2200 and monthly raise of $105 during his first year of training.

∴ a = 2200 and d = 105

Since the general form of A.P is,

a, a + d, a + 2d, a + 3d, .............

Where,   is the last term of A.P or his monthly salary at the end of his training and n is the number of terms in a series.

So, the A.P is:

2200, 2200 + 105, 2200 + 2(105) .........

2200, 2305, 2410 ............

Since there is 12 month in a year therefore, n = 12.

. = 2200 + ( 12 - 1) × 105

= 2200 + 11 × 105

= 2200 + 1155

= 3355

∴ . = 3355

So the monthly salary of Jose at the end of his training is 3355$.

35,38,41,44,47,50,

Step-by-step explanation:

n ∈N means that n is an element of Natural numbers

Natural numbers are whole non-negative numbers

n ≥ 1, means that n = 1, 2, 3, 4, 5, 6,

tn = 32 + 3n

the first term t1 = 32 + 3(1)

                            32 + 3 = 35

the second term t2 = 32 + 3(2)

                                   32 + 6 = 38

the third term t3 = 32 + 3(3)

                              32 + 9 = 41

D) 35, 38, 41, 44, 47, 50, ...

Step-by-step explanation:

tₙ  = 32 + 3n; n ∈ N, n ≥ 1

t₁  = 32 + 3(1) = 32 +  3 = 35

t₂ = 32 + 3(2) = 32 +  6 = 38

t₃ = 32 + 3(3) = 32 +  9 = 41

t₄ = 32 + 3(4) = 32 + 12 = 44

t₅ = 32 + 3(5) = 32 + 15 = 47

t₆ = 32 + 3(6) = 32 + 18 = 50

The sequence starts at t₁ = 35 and each term is 3 units greater than the preceding term.

The sequence is 35, 38, 41, 44, 47, 50, ...

D) 35, 38, 41, 44, 47, 50,...

Step-by-step explanation:

The general term of an arithmetic sequence is

, where n ∈N and n ≥ 1.

When n=1,

When n=2,

When n=3,

When n=4,

When n=5,

When n=6,

Hence the sequence is 35, 38, 41, 44, 47, 50,...

The correct answer is D