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A computer generated a sequence \(A\) of numbers using the following formula: \(A_n = A_1 + (n-1)d\)

\(d\) is the common difference between any two consecutive terms of the sequence \(A\)

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

I had the same issue. Because it said consecutive, I assumed d = 1. Are we wrong in some way?

When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, .... For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.

But in the original question, stem says consecutive terms of the sequence A (which is given to be arithmetic progression) and not consecutive integers, so the common difference is not necessary to be 1 in this case.

As for the question:

A computer generated a sequence \(A\) of numbers using the following formula: \(A_n = A_1 + (n-1)d\). \(d\) is the common difference between any two consecutive terms of the sequence \(A\). If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence? A. 3 B. 2 C. 1 D. -1 E. -3

its AP A, A+d,A+2d,A+3d,.........,A+(n-1)d sorry I cant able to write the equation here but its a simple problem solve 2 equations for 2 unknowns(A and d)

ThinkingHat wrote:

Quote:

A computer generated a sequence \(A\) of numbers using the following formula: \(A_n = A_1 + (n-1)d\)

\(d\) is the common difference between any two consecutive terms of the sequence \(A\)

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers \(A\)using the following formula:

\(An = A1 + (n-1)d\) where \(d\)is the common difference between any number and the next number in the set \(A\).
_________________

its AP A, A+d,A+2d,A+3d,.........,A+(n-1)d sorry I cant able to write the equation here but its a simple problem solve 2 equations for 2 unknowns(A and d)

ThinkingHat wrote:

Quote:

A computer generated a sequence \(A\) of numbers using the following formula: \(A_n = A_1 + (n-1)d\)

\(d\) is the common difference between any two consecutive terms of the sequence \(A\)

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

An=A1-(n-1)d is the formula for nth term in an arithmetic progression. hence 7th term A7=A1-(7-1)d Similarly,2nd term A2=A1-(2-1)d 3rd term A3=A1-(3-1)d and 5th term A5=A1-(5-1)d

Now According to question,A2+A5=8 i.e 2A1+5d=8 and A3+A7=14 i.e, 2A1+8d=14

The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers \(A\)using the following formula:

\(An = A1 + (n-1)d\) where \(d\)is the common difference between any number and the next number in the set \(A\).

I agree... Can someone please provide a resolution for this...

The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers \(A\)using the following formula:

\(An = A1 + (n-1)d\) where \(d\)is the common difference between any number and the next number in the set \(A\).

I agree... Can someone please provide a resolution for this...

I had the same issue. Because it said consecutive, I assumed d = 1. Are we wrong in some way?
_________________

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A computer generated a sequence \(A\) of numbers using the following formula: \(A_n = A_1 + (n-1)d\)

\(d\) is the common difference between any two consecutive terms of the sequence \(A\)

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?