The answer will be:476/19, 404/19, 332/19,...so on.Step-by-step explanation:We have given; S10 = 80; and, S10-20 (i.e, next 10 term of a10) = -280;The formula of adding A.P. to n term is given as; = (n/2)(a + al) [here, al is the last term] or, = (n/2)(a + a +d(n-1))Hence, for S10, the EQUATION we can write is; = (n/2)(a + a +d(n-1)) = 80; = (10/2)(a + a +d(10-1)) = 80; = 5 (2a + 9d) = 80; = 2a + 9d = 16; (i)For the sum of the next 10 TERMS from a10 or S10-20, the formula will change to: = (n/2)(a10 + a20) (II) ( here, a10 will become first term and a20 will be the last term. )Thus, for equation (ii); a10 = a + d(10 - 1); = a + 9d; (iii)and, a20 = a + d(20 - 1); = a + 19D; (iv)Here, the terms will remain 10 because we are using the next 10 terms from a10.So, n = 10. (for eqaution (ii)) (v)Now, put the value of equation (iii), (iv), (v) and S10-20, in equation (ii); = (n/2)(a10 + a20) = -280; = (10/2)(a +9d + a + 19d) = -280; = 5 (2a + 28d) = -280; = 2a + 28d = -56; (vi)Using substitution method in equation (i) and (ii), we can write; = (16 - 9d) + 28d = -56; = 16 + 19d = -56; = d = (-56 -16) / 19; = -72/19;Hence, using the value of d and equation (i), we can derive the value of a.Thus, = 2a + 9(-72/19) = 16; = 2a = 16 - 9(-72/19); = 2a = 16 - (-648/19); = 2a = 952/19 = a = 476/19;Therefore, the A.P. will be :476/19, 404/19, 332/19,...(I believe you can proceed this A.P. now)Verify: We had given; S10 = 80;Lets put the value of a and d in the formula of adding A.P.; = (n/2)(a + a +d(n-1)) = 80; = (10/2){(476/19) + (476/19) + (-72/19)(10-1)} = 80; = 5 {(952/19) + (-648/19)} = 80; = 5 { (952-648)/19} = 80; = 5 {304 / 19} = 80; = 5 (16) = 80; = 80 = 80. = RHS = LHSHence, verified.We had given; S10-20 = -280;Lets put the value of a and d in the formula of adding A.P.; = (10/2)(a10 + a20) = -280; = (10/2)(a + d(10-1) + a + d(20-1)) = -280; = (5)(a + 9d + a + 19d) = -280; = ((476/19) + 9(-72/19) + (476/19) + 19(-72/19)) = -56; = ((952/19) + (-648/19) + (-1368/19)) = -56; = ((952 - 648 - 1368) / 19) = -56; = (-1064 / 19) = -56; = - 56 = -56 = RHS = LHSHence, verified. That's all.