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Each term of A.P is doubled. Is the resulting sequence also an A.P ? If it is write its first term.
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Step-by-step solution
5 stepsWrite the expressions for the and terms of an A.P.
Let the first term be and the common difference be . The term of an A.P. is given by .
The term is .
The term is .Set up the equation based on the given condition.
The problem states that 7 times the term is equal to 11 times the term:
Substitute the expressions from Step 1:
Solve the equation for in terms of .
Subtract from both sides:
Subtract from both sides:
Divide by 4:
Find the expression for the term.
The term is .
Substitute the value of from Step 3 into the expression for the term.
Thus, the term of the A.P. is .
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