Question

What is the sum of the first 9 terms of an arithmetic progression if the first term is 7 and last term is 55?

Answer 1

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Answer 2

Given:

We have given that the first term is 7 and last term is 55.

To Find:

We have to find the sum of the first 9 terms of an arithmetic progression?

Step-by-step explanation:

• We have given the first term of A.P is 7 which means a=7.
• The last term of the A.P is 55 which is denoted by
• We know the last term of the A.P is given by the formula

       $a_n=a+(n-1)d$

• We have a number of terms is 9 put all the values in above equation.

        $55=7+(9-1)d$

• Now simplify the equation above written to get the values of d.

       $55=7+8d$

• Now take the like terms together and simplify them.

       $48=8d\\d=6$

• Hence, we get the value of d is 6 which is common difference.
• Now for calculating the value of sum of 9 terms of A.P we know sum of n terms of A.P is given by the formula

       $S_n=\frac{n}{2} (2a+(n-1)d)$

• We have a=7,d=6,n=9 put these values in the above equation.

        $S_9=\frac{9}{2} (2(7)+(9-1)6)$

• Now simplify the equation by solving the brackets.

         $S_n=\frac{9}{2} (14+48)\\S_n=\frac{9}{2} \times62\\S_n=9\times31\\S_n=279$

Hence, the sum of n terms of A.P is 279.