Question

Find the sum of first twenty terms of arithmetic series 2+7+12+............... using suitable formula

Answer 1

Answer:

990

Step-by-step explanation:

This is an arithmatic series.

It has common diff, d = 5

and first term, a1 = 2

Sum of n arithmatic terms is given by,

S_n

= (n/2)(2a1 + (n - 1)d)

Here, n = 20

S_20

= 10(4 + 19*5)

= 10(99)

= 990

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{s_{20}=990}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt:\implies A.P = 2 + 7 + 12+...... \\ \\ \tt: \implies No. \: of \: terms = 20\\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Sum \: of \: 20 \: terms =?$

• According to given question :

$\tt \circ \: First \: term=2 \\ \\ \tt \circ \: Common \: difference = 5 \\ \\ \tt \circ \: No. \: of \: terms = 20 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies s_{n} = \frac{n}{2} \bigg(2a +( n - 1)d \bigg) \\ \\ \tt: \implies s_{20} = \frac{20}{2} \times \bigg(2 \times 2 + (20 - 1) \times 5 \bigg) \\ \\ \tt: \implies s_{20} =10 \times (4 + 95) \\ \\ \tt: \implies s_{20} =10 \times 99 \\ \\ \green{\tt: \implies s_{20} =990 } \\ \\ \green{\tt \therefore Sum \: of \: 20 \: terms \: is \: 990}$