Question

3. (a.) The 12th term of a linear sequence is 74 and the sum of the first three terms is 42, Find (i.) the first term and the common difference (ii.) the sum of the first 10th terms of the sequence. pls answer it is urgent pls​

Answer 1

The 12th term = a + 11d where a is the first term and d is the common difference
a + 11d = 74

The first three terms are a, a + d, a + 2d
a + (a + d) + (a + 2d) = 42
3a + 3d = 42
a + d = 42 / 3 = 14
By subtracting this equation from the T12 equation
(a + 11d) - (a + d) = 74 - 14
10d = 60
d = 6 (the common difference = 6)
a + 6 = 14
a = 14 - 6 = 8 (the first term = 8)

S(n) = n/2 x (2a + (n-1)d)
S(10) = 10/2 x (2x8 + (10-1)x6)
S(10) = 5 x (16 + 54) = 5 x 70 = 350