What is the sum of each arithmetic series 50+44+38+....+8? - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

The series of arithmetic sequence which is

50, 44, 38, . . . . 8

The arithmetic expression is expressed as The first term be

t 1_{}

and the difference be
Where

d = t 2 - t 1 = t 3 - t 2 = t 4 - t 3

The formula is

tn = t 1 + (n - 1) d

t 1 = 50, d = t 2 - t 1 = 44 - 50 = 6

The general formula for n terms is S

{{n = \frac{n}{2}}_{} = [2 t 1 + (n - 1) d] .}_{}

If 8 be the

k^{th}

term of the series , then

tk = t 1 + (k - 1) d .

⇒

tk = t 1 + (k - 1) d

⇒

8 = 50 + (k - 1) - 6

⇒

6 (k - 1) = 50 - 8 = 42

⇒

k = \frac{42}{6} + 1 = 8 .

The sum of the series

S

= \frac{8}{2} [2 \times 50 - 6 (8 - 1)] = 232 .

What is the sum of each arithmetic series $50 + 44 + 38 + . . . . + 8 ?$