How many terms are in an arithmetic sequencewhose first term is -3, common difference is 2, andast term is 23?. Find the common difference of the arithmeticsequence with fourth term is 10 and eleventh term45.
Answer (1)
Problem 1 - Formula: The general formula for the nth term of an arithmetic sequence is: an = a1 + (n - 1)dwhere:- an is the nth term- a1 is the first term- d is the common difference- n is the number of terms- Applying the formula: a1 = -3d = 2an = 23- We need to find n- Solving for n: 23 = -3 + (n - 1)223 = -3 + 2n - 223 = 2n - 528 = 2nn = 14-Answer: There are 14 terms in the arithmetic sequence. Problem 2 - Applying the formula: a4 = 10a11 = 45- Setting up equations: 10 = a1 + 3d (Since the fourth term is a4)45 = a1 + 10d (Since the eleventh term is a11)Solving for d: Subtract the first equation from the second equation:35 = 7dd = 5- Answer: The common difference of the arithmetic sequence is 5HOPE IT HELPS YOU
