SOLUTION: the sum of the first four terms of a linear sequence(A.P)is 26 and that of the next four terms is 74. Find the value of: (¡) the first term; (¡¡) the common difference.

Question 1162919: the sum of the first four terms of a linear sequence(A.P)is 26 and that of
the next four terms is 74. Find the value of:
(¡) the first term;
(¡¡) the common difference.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
the sum of the first four terms of a linear sequence(A.P)is 26 and that of
the next four terms is 74. Find the value of:
(¡) the first term;
(¡¡) the common difference.

From 3 and 6, we have Solve that system for first term a₁ and common difference d. Edwin

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

The sum of the first 4 terms is + + + . The sum of the next 4 terms is + + + . Each difference , , and is equal to 4d, where d is the common difference of the AP. Therefore, 4*(4d) = 74 - 26, or 16d = 48; hence, d = 48/16 = 3. Next, 26 = 4a + (1+2+3)d = 4a + 6*3 = 4a + 18, which implies 4a = 26 - 18 = 8. Answer. The first term of the AP is 8/4 = 2; the common difference is 3.

Solved.

The goal of this problem is to teach you manipulate with AP terms quickly and informally.

It is a simple problem; so, the method of its solution should be adequately simple.

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On arithmetic progressions, see the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions
    - Calculating partial sums of arithmetic progressions
    - Finding number of terms of an arithmetic progression
    - Advanced problems on arithmetic progressions
    - Problems on arithmetic progressions solved MENTALLY
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

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Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

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