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In each of the following APs the 1st, 2nd and last terms are given. Find the common difference the number of terms in each sequence.
ScanSolve AI Answer
Step-by-step solution
10 stepsHere are the common differences and number of terms for each arithmetic progression:
The general formula for the -th term of an arithmetic progression (AP) is , where is the first term, is the common difference, and is the number of terms. The common difference can be found using .
Part a· 2 steps
1, 5, ..., 69
Find the common difference .
Find the number of terms .
The common difference is and the number of terms is .
Part b· 2 steps
80, 83, ..., 152
Find the common difference .
Find the number of terms .
The common difference is and the number of terms is .
Part c· 2 steps
98, 91, ..., 0
Find the common difference .
Find the number of terms .
The common difference is and the number of terms is .
Part d· 2 steps
2.3, 3.4, ..., 21
Find the common difference .
Find the number of terms .
The common difference is and the number of terms is .
Part e· 2 steps
6, -2, ..., 71
Find the common difference .
Convert to a decimal: .
Find the number of terms .
The common difference is and the number of terms is .
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