document.write( "Question 1189392: 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 values of (i)the first term (ii)the common difference. \n" ); document.write( "
Algebra.Com's Answer #820736 by greenestamps(13203)\"\" \"About 
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\n" ); document.write( "I will provide a response that solves the problem a bit more informally than the other tutor....

\n" ); document.write( "Each of terms 5-8 is equal to the corresponding term among the first four terms, plus 4 times the common difference. (The 5th term is 4 terms after the 1st, so it is equal to the first term plus 4 times the common difference; likewise for the other pairs of corresponding terms.)

\n" ); document.write( "So the difference between the sum of the first four terms and the second four terms is 4*4=16 times the common difference.

\n" ); document.write( "The difference between those sums is 48, so the common difference in the sequence is 48/16=3.

\n" ); document.write( "Using a for the first term, and using the common difference of 3, the first four terms are

\n" ); document.write( "a, a+3, a+6, a+9

\n" ); document.write( "The sum of those first four terms is 26:

\n" ); document.write( "(a)+(a+3)+(a+6)+(a+9) = 26
\n" ); document.write( "4a+18=26
\n" ); document.write( "4a=8
\n" ); document.write( "a=2

\n" ); document.write( "ANSWERS: The first term is 2; the common difference is 3
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