Help me please solving this SERIES question

evaluate the sum of the first 20 terms of the series 5 -2 +10 -8 +15 -32+...

5, 10, 15... form an arithmetic sequence.

S10 = 10/2[2(5) +9(5)]
s10= 5(55)
S10 = 275
while
-2, -8,-34...form geometric sequence.

S10 = -2[1- (4)^10]/[1-4
S10 = -699050

S20 = 275 -699050
S20= -698775

sum:

(5+10+15...`0 terms)-(2+8+32+...10 terms)
= 10/2(10+9(5)) - [2(1-4^10)/(1-4)]
= 275- (2/3(1048575))
= 275-699050
=-698775

1st pat is ap
2nd part is gp

: )

sum of the first 20 terms of the series 5 -2 +10 -8 +15 -32+...
= (5 + 10 + 15 + .... 10 terms ) -- (2 + 8 + 32 + .... 10 terms)
= (10/2)[2*5 + (10 -- 1)*5] -- 2[4^10 -- 1] / (4 -- 1)
= 275 -- 682
= -- 407 ANSWER

2

thanks i needed that