Find the sums given below:(1) 34+32+30+..........+10(2) -5+(-8)+(-11)+

1.	Find the sums given below:(1) 34+32+30+..........+10(2) -5+(-8)+(-11)+..........+(-230)
Answer» $S_n = \frac{n}{2} [T_1 + T_n] \\ \\ n = \frac{T_n - T_1}{d} + 1$ n = no. of terms d = common DIFFERENCE 1. $d = 32 - 34 = - 2$ $T_1 = 34 \\ T_n = 10$ $n = \frac{10 - 34}{- 2} + 1 \\ \\ = \frac{- 24}{- 2} + 1 \\ \\ = 12 + 1 = 13$ $S_n = \frac{13}{2} [34 + 10] \\ \\ = \frac{13}{2} \times 44 = 13 \times 22 = 286$ 2. $d = (- 8) - (- 5) = - 8 + 5 = - 3$ $T_1 = - 5 \\ T_n = - 230$ $n = \frac{(- 230) - (- 5)}{- 3} + 1 \\ \\ = \frac{- 230 + 5}{- 3} + 1 \\ \\ = \frac{- 225}{- 3} + 1 \\ \\ = 75 + 1 = 76$ $S_n = \frac{76}{2} [(- 5) + (- 230)] \\ \\ = \frac{76}{2} [- 5 - 230] \\ \\ = \frac{76}{2} \times (- 235) = 38 \times (- 235) = - 8930$ Hope these may be helpful. PLEASE MARK my answer as the brainliest if these may be helpful. Thank you. Have a nice DAY.