Question

If the nth term of an AP is 9-5n . Find the sum of first 10terms.​

Answer 1

Answer:

-185

Step-by-step explanation:

Given that the nth term of the AP is 9 - 5n

First, assume the value of n in the nth term. Assume nth term = 1st term. According to the question, nth term = 9 - 5n. Similarly :

1st term = 9 - 5( 1 )

1st term = 9 - 5

1st term = 4

Now again assuming the value of n in nth term. Assuming nth term = 10th term. Similarly :

10th term = 9 - 5( 10 )

10th term = 9 - 50

10th term = - 41

S10 = (10)÷(2)[ 4 + ( - 41 ) ]

S10= 5[ 4 - 41 ]

S10= 5( - 37)

S10= -185

S10=210[4+(−41)]

S10=5[4−41]

S10=5(−37)

S10=−185

Therefore, Sum of 10 terms of the AP is - 185.

Answer 2

Answer:

Value of $n^{th}$ term = 9 - 5n

       $a_{n}$ = 9 - 5n

   Therefore we can other terms too

      $a_{1}$ = a = 9 - 5 × 1

          = 9 - 5 = 4

     $a_{2}$ = 9 - 5 × 2

         = 9 - 10 = -1

Common difference = $a_{2\\}$ - $a_{1}$

                                  = -1 - 4

                                  = -5

Sum of first 10 terms = $\frac{n}{2}${2a + (n-1) d}

                 $S_{10\\}$            = $\frac{10}{2}$ {2× 4 + (10 - 1)-5}

                                  = 5 (8 - 45)

                                  = 5 × -37  

                                  = -185