Question

The algebraic form of an arithmetic sequence is 4n+3
a.what is the sum of its first and 20th term?
b.wgat is the sum of first 20 terms of this sequence?​

Answer 1

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

$\green{\tt{\therefore{Sum\:of\:first\:and\:20th\:term=90}}}$

$\green{\tt{\therefore{Sum\:of\:first\:20\:term=900}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies A.P = 4n + 3 \\ \\ \green{\underline \bold{Given :}} \\ \tt: \implies Sum \: of \: first \: and \: 20th \: term =? \\ \\ \tt: \implies Sum \: of \: first \: 20 \: terms =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt:\implies a_{n} = 4n + 3 \\ \\ \tt:\implies a_{1} =4 \times 1 + 3 \\ \\ \green{\tt:\implies a_{1} =7} \\ \\ \bold{Similarly:} \\ \tt:\implies a_{2} = 4 \times 2 + 3 \\ \\ \green{\tt:\implies a_{2} = 11} \\ \\ \bold{Similarly : } \\ \tt:\implies a_{3} = 4 \times 3 + 3 \\ \\ \green{\tt:\implies a_{3} =15} \\ \\ \green{\tt \circ \: Common \: difference = 4} \\ \\ \bold{For \: sum \: of \:first \: and \: 20th \: term : } \\ \tt: \implies a_{1} + a_{20} = 7 +( 7 + 19 \times 4) \\ \\ \tt: \implies a_{1} + a_{20} =7 + 83 \\ \\ \green{\tt: \implies a_{1} + a_{20} =90} \\ \\ \bold{For \: sum \: of \: first \: 20 \: term : } \\ \tt: \implies s_{n} = \frac{n}{2} (2a + (n - 1)d) \\ \\ \tt: \implies s_{20} = \frac{20}{2} (2 \times 7 + (20 - 1) \times 4) \\ \\ \tt: \implies s_{20} = 10 \times (14 + 76) \\ \\ \tt: \implies s_{20} = 10 \times 90 \\ \\ \green{\tt: \implies s_{20} = 900}$

Answer 2

Answers :

sum of first and 20th term = 90

sum of first 20 terms = 900

Step-by-step explanation:

Given:

⟹A.P=4n+3

Given:

⟹ Sum of first and 20th term=?

⟹ Sum of first 20 terms=?

➡️ According to the question ,

As we know that ,

⟹ an =4n+3

⟹ a1 =4×1+3

⟹ a1 =7

Similarly:

⟹ a2 =4×2+3

⟹ a2 = 11

Similarly :

⟹ a3 =4×3+3

⟹a3 =15

∘Common difference = 4

For sum of first and 20th term

⟹ a1 + a20 = 7 + ( 7 + 19 × 4 )

⟹ a1 + a20 = 7 + 83

⟹ a1 + a20 = 90

For sum of first 20 terms

⟹ Sn = n/2 (2a + (n-1) d )

⟹ S20 = 20/2 ( 2×7 + ( 20 - 1 ) × 4 )

⟹ S20 = 10 ( 14 + 76 )

⟹ S20 = 10 × 90

⟹ S20 = 900