For the arithmetic progressions write the first term a and the common

1.	For the arithmetic progressions write the first term a and the common difference d:\(\frac{1}{5}\), \(\frac{3}{5}\), \(\frac{5}{5}\), \(\frac{7}{5}\), ………….
Answer» Given arithmetic series is \(\frac{1}{5}\), \(\frac{3}{5}\), \(\frac{5}{5}\), \(\frac{7}{5}\), …………. It is seen that, it’s of the form of \(\frac{1}{5}\), \(\frac{3}{5}\), \(\frac{5}{5}\), \(\frac{7}{5}\), …………. a, a + d, a + 2d, a + 3d, Thus, by comparing these two, we get a = \(\frac{1}{5}\), a + d = \(\frac{3}{5}\), a + 2d = \(\frac{5}{5}\), a + 3d = \(\frac{7}{5}\) First term (a) = \(\frac{1}{5}\) By subtracting first term from second term, we get d = (a + d)-(a) d = \(\frac{3}{5}\) – \(\frac{1}{5}\) d = \(\frac{2}{5}\) ⇒ common difference (d) = \(\frac{2}{5}\)

For the arithmetic progressions write the first term a and the common difference d:\(\frac{1}{5}\), \(\frac{3}{5}\), \(\frac{5}{5}\), \(\frac{7}{5}\), ………….

Answer»

Given arithmetic series is \(\frac{1}{5}\), \(\frac{3}{5}\), \(\frac{5}{5}\), \(\frac{7}{5}\), ………….

It is seen that, it’s of the form of \(\frac{1}{5}\), \(\frac{3}{5}\), \(\frac{5}{5}\), \(\frac{7}{5}\), …………. a, a + d, a + 2d, a + 3d,

Thus, by comparing these two, we get

a = \(\frac{1}{5}\), a + d = \(\frac{3}{5}\), a + 2d = \(\frac{5}{5}\), a + 3d = \(\frac{7}{5}\)

First term (a) = \(\frac{1}{5}\)

By subtracting first term from second term, we get

d = (a + d)-(a)

d = \(\frac{3}{5}\) – \(\frac{1}{5}\)

d = \(\frac{2}{5}\)

⇒ common difference (d) = \(\frac{2}{5}\)