The 8th term of an A.P., whose first two terms are - 5 and 2 respectively, is :
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Step-by-Step Solution
Step 1: Identify the first term and common difference
In an Arithmetic Progression (A.P.), the first term is denoted by a1 and the common difference by d. We are given the first two terms, a1=−5 and a2=2. The common difference d is found by subtracting any term from its succeeding term.
Step 2: Calculate the common difference
Substitute the given values of the first and second terms into the formula for the common difference. Subtracting −5 from 2 gives 2+5, which simplifies to 7. So, the common difference is 7.
Step 3: Apply the formula for the nth term
The formula for the n -th term of an Arithmetic Progression is an=a1+(n−1)d, where an is the n -th term, a1 is the first term, n is the term number, and d is the common difference. We need to find the 8th term, so n=8.
Step 4: Calculate the 8th term
Substitute the values a1=−5, n=8, and d=7 into the formula for the n -th term. First, calculate (8−1), which is 7. Then multiply 7 by the common difference 7 to get 49. Finally, add this to the first term, −5, to find the 8th term.