Answers

2015-07-07T21:42:19+08:00
Common difference is 6.
Solution below. (sorry for the handwriting) 
0
2015-07-07T21:59:30+08:00

Note that you are given the following data:

S=530 \\ A_{10} = 80 \\ n=10

You are asked of the 1st term(A1) and the common difference(d).

 In finding the nth term of an arithmetic progression, we use the formula:

A_n = A_1 + (n-1)d

Using the given data we'll have:

A_10 = A_1 + (n-1)d \\ 80 = A_1 + (10-1)d \\ 80 = A_1 + 9d \\ A_1 = 80 - 9d~~~~~~----equation1

In finding the Sum of all the terms, we use the formula:

S = (2A_1 + (n-1)d) \frac{n}{2}

Substituting the given values we'll have:

530 = (2A_1 + (10-1)d) \frac{10}{2} \\ 530 = (2A_1 + 9d) 5 \\ Dividing~ the~ whole ~equation ~by ~5~ we'll~ have: \\ 106 = 2A_1 + 9d ~~~~~~~-----equation2

Substitute equation 1 to equation 2

106 = 2A_1 + 9d \\ 106 = 2(80-9d) + 9d \\ 106 = 160 - 18d + 9d \\ 106 - 160 = -18d + 9d \\ -54 = -9d \\ 6 = d ~~~~~or \\ d = 6 \\ \\ Substitute~to~equation1 \\ A_1 = 80-9d \\ A_1 = 80 -9(6) \\ A_1 = 80-54 \\ A_1 = 26

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