Two A.P.s have the same first term. The common difference of the first A.P. is -3 and of the second A.P. is -5. The difference of the 6th term of the second A.P. from that of the first A.P. is :
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Step-by-Step Solution
Step 1: Define the terms of an A.P.
We start by recalling the formula for the nth term of an arithmetic progression (A.P.), where an is the nth term, a is the first term, and d is the common difference.
Step 2: Express the 6th terms for both A.P.s
Let a be the common first term for both A.P.s. For the first A.P., the common difference is d1=−3. For the second A.P., the common difference is d2=−5. We substitute these values into the formula to find the 6th term for each A.P.
Step 3: Calculate the difference between the 6th terms
The problem asks for the difference of the 6th term of the second A.P. from that of the first A.P., which means we need to calculate a1,6−a2,6. We substitute the expressions we found for each 6th term.
Step 4: Simplify the expression
We simplify the expression by distributing the negative sign and combining like terms. The first term a cancels out, leaving us with the final difference.