Question

nth term of an AP is given by an expression 7n-2,find the common difference of this sequence if fisrt term of sequence is 1? a.2 b.-2 c-7 d7​

Answer 1

Explanation:

there is something wrong with what your write here as problem description.

either there is something missing in the main expression, or in the answer options.

given your nth-term expression 7n-2, none of the 4 answer options can fit.

so, I thought, maybe there was a typo.

the possible interpretations of the expression could be

7n - 2

7(n-2)

`{7}^(n) - 2`

`{7}^(n - 2)`

we know that

a1 = 1

a2 = either

a1 + 2 = 3

a1 - 2 = -1

a1 + 7 = 8

a1 - 7 = -6

so, we can eliminate both negative answer options, because they would cause only negative sequence elements, but the main expression (neither of the 4 possibilities) does not allow that.

but also none of the 4 possibilities of the expression delivers any of the 4 values for a2 as described above.

7×2 - 2 = 14 - 2 = 12

7(2-2) = 7×0 = 0

7² - 2 = 49 - 2 = 47

`{7}^(2 - 2) = {7}^(0) = 1`

similar not for a3.

so, if I consider your answer options right, we have 4 possible arithmetic sequences:

1. 1, 3, 5, 7, 9, 11, 13, 15, ...

2. 1, -1, -3, -5, -7, -9, -11, -13, ...

3. 1, 8, 15, 22, 29, 36, 43, 50, ...

4. 1, -6, -13, -20, -27, -34, -41, ...

the nth term expression is for

a. an = 2n - 1

b. an = 2×(-n) + 3 = 2×(-n + 1) + 1

c. an = 7n - 6

d. an = 7×(-n) + 8 = 7×(-n + 1) + 1

so, please pick the right expression from this list, and then use the answer option with the same letter.