Question

Find the sum of first 20th terms of arithemetic sequence 5, 9, 13

Answer 1

Step-by-step explanation:

sn=n/2(2a+(n-1)d

S20=10(10+(19)4

= 10(10+76)

s20=860

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Answer 2

Answer:

$\bigstar{\bold{S_{20}=860}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• A.P is 5, 9, 13.....

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Sum of first 20 terms of the A.P

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we need to find out the common difference(d) of the A.P

  d = a₂ - a₁

→ Here a₂ = 9, a₁ = 5

   d = 9 - 5 = 4

→ The 20th term of the A.P is given by

  a₂₀ = 5 + 19 × 4

  a₂₀ = 81

→ Sum of 20 terms is given by the formula,

  $S_n=\dfrac{n}{2} (a_1+a_n)$

where n =20

$S_{20}=\dfrac{20}{2}(5+81)$

S₂₀ = 10 × 86

S₂₀ = 860

$\boxed{\bold{S_{20}=860}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The last term of an A.P is given by

   $a_n=a_1+(n-1)\:d$

→ Sum of n terms of a A.P is given by

  $S_n=\dfrac{n}{2} (a_1+a_n)$

  $S_n=\dfrac{n}{2} (2a_1+(n-1)\:d\:)$