Question

find the sum of the terms of each arithmetic sequence:
1.) 53, 54, 55, 56, ..., 100 (n = ?; Sn = ?)
2.) -17, -11, -5, ......, 79 (n = ?; Sn = ?)
3.) -3, 2, 7, ...... 20 terms (a20 = ?; S20= ?)
4.) 7, -1, -9, ...... 180 terms (a18 = ?; S18 = ?;)
5.) if d=2, n=7, an= 40, find a1 and Sn?

Answer 1

Answer:

1.68

2.59

3. 12

4.-34

5.?

Answer 2

Answer:

1.)53+54+55+56+ ... +100

let  a = 53 ,l = 100, and common difference (cd) =1

then,  $A_{n}$= a+(n-1)d  

            100 =   53 +(n-1) 1       $S_{n}$ = $\frac{n}{2}$ (a + l)                                                                                              

             100 = 53+ n-1                 = $\frac{48}{2}$ (53+100)

             100 = 53-1+n                  = 24 (153)

             100= 52+n                      = 24×153

               100-52= n                      = 3672

               n = 48