Can someone please solve these questions about arithmetic sequences? Thanks in advance!?

1,

The sequence is 4, 8, 12, 16

so the nth term = 4 + (n-1)*4 = 4 + 4n -4 = 4n

so check if the term as divisible by 4 .

(a)246

(b)264

(c)288

(d) 324

(e)380

The answer is (a)

because 264= 66*4 ;288=72*4 ; 324 = 81*4 ; 95*4 = 380

However (a) 246 = 61.5* 4 , so it is not evenly divided by 4.

2.

(x-7), 2, x+3

for this to be arithmetic sequence, the difference between the 1st and 2nd

must equal the difference between the 2nd and 3rd number

2 - (x-7) = (x+3) - 2

9 - x = x + 1

add x to both sides

9 = 2x + 1

add -1 to both sides

2x = 8

x = 4

checking

4 -7 = -3

4+3 = 7

so sequence -3, 2, 7

x= 5

answer = (D) 5

3.

This question is about a geometric sequence with

a_1 = 9/4 and r = (2/3)

a_n = a_1*r^*(n-1) = (9/4)* (2/3)^(n-1)

so a_7 = (9/4)*(2/3)^6 = (9/4)*(2^6/3^6)= (3^2/3^6) *(2^6/2^2) =

(2^4/3^4) = 16/81

so answer is (B) 16/81

4. If 5th term = 2 , and 9th term = - 10

what is the 1st term of this arithmetic sequence

so formula is

a_n = a_1 + (n-1)*d

a_5 = a_1 + 4d

a_9 = a_1 + 8d

a_9 -a_5 = a_1 +8d - a_1*4d = 4d

-10 - (-2) = -8 = 4d

4d = -8

d = -8/4 = -2

so a_5 = a_1 + 4d

-2 = a_1 + 4* (-2) = a_1 - 8

a_1 = 8 + -2 = 6

a_1 = 6

so sequence is

6, 4, 2, 0 , -2 , -4, -6, -8 , -10

so answer is first term is 6

(a) 4 is the answer

5.

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