Question

find the sum of the series 1+1 3/4+2 1/2+..........to 20terms​

Answer 1

Answer:-

Given:

a(first term) = 1

d ( Common difference) = t(n) - t(n - 1)

=> t(2) - t(1)

$=> 1 \frac{3}{4} - 1 \\ \\ = > \frac{7}{4} - 1 \\ \\ = > \frac{7 - 4}{4} \\ \\ d = \frac{3}{4}$

n ( number of terms) = 20.

We know that,

$S _{n} = \frac{n}{2} [2a + (n - 1)d] \\ \\ S _{20} = \frac{20}{2} [2 \times 1 + (20 - 1) (\frac{3}{4} )] \\ \\ = > 10(2 + \frac{19 \times 3}{4} ) \\ \\ = > 10( \frac{8 + 57}{4} ) \\ \\ = > \frac{650}{4} \\ \\ S_{20} = 162.5$

Therefore, the sum of first 20 terms of the given sequence is 162.5.