Find the sum of the first 23 terms of the arithmetic sequence 4m-3,-10,….

Question

Find the sum of the first 23 terms of the arithmetic sequence 4m-3,-10,...

Answer 1

d = common difference = -10-(4m-3) = -7-4m

nth term = an = a1 + (n-1)d = 4m-3 + (n-1)(-7-4m)

23rd term = a23 = 4m-3 + 22(-7-4m) = 4m-3 - 154 - 88m = - 157 - 84m

sum of n terms = sn = (n/2)(a1+an)

sum of 23 terms = s23 = (23/2)(4m-3 -157-84m) = (23/2)(-160 - 80m) = -1840-920m

the sum of the first 23 terms = -1840 -920m