Question

Find the sum of first twenty terms of the ap series

1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 , 25.......​

Answer 1

✬ Sum = 590 ✬

Step-by-step explanation:

Given:

• AP series is 1, 4 , 7 , 10.....

To Find:

• Sum of first 20 terms of AP ?

Solution: As we know that sum of n terms of an AP series is given by

★ Sⁿ = n/2 × (2a + (n – 1)d ★

Here we have

• a = first term = 1
• d = common difference = 4 – 1 = 3
• n = number of terms

Put all the values on the formula

$\implies{\rm }$ S²⁰ = 20/2(2 × 1 + (20 – 1)3

$\implies{\rm }$ S²⁰ = 10 × (2 + 19 × 3)

$\implies{\rm }$ S²⁰ = 10 × (2 + 57)

$\implies{\rm }$ S²⁰ = 10 × 59

$\implies{\rm }$ S²⁰ = 590

Hence, sum of first 20 term of given AP is 590.

Answer 2

$\blue{ \rm{Given:-}}$

◉ Ap series is 1, 4, 7, 10, 13, 16, 19........

$\blue{ \rm{To \: Find:-}}$

◉ Sum of first twenty terms of the AP series.

$\blue{ \rm{Solution:- }}$

By using formula,${\rm{\boxed{S_n = \frac{n}{2} [2a + (n - 1)d]}}}$

We have,

◕ $\rm{S_n = Sum \: of \: n \: terms}$

◕ $\rm{a = first \: term = 1 }$

◕$\rm{d = common \: difference = 4 - 1 = 3}$

◕ $\rm{n = number \: of \: terms}$

Put the values in the formula,

We get,

☞ $\rm{S_{20} = \frac{20}{2} [2 \times 1 + (20 - 1) \times 3]}$

$= 10 [2 + 19 \times 3]$

$= 10[2 + 57]$

$= 10 \times 59$

$= 590$

∴ Sum of first twenty terms = $\green{ \underline{ \boxed{ \rm{ 590}}}}$

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Is it an AP?

Yes☑

Given series is 1, 4, 7, 10, 13, 16, 19, 22, 25....

Since,4 - 1 = 7 - 4 = 10 - 7 , and so on.....

i.e., 3 = 3 = 3.......

Given the common difference is 3.

Therefore, the given sequence is an AP.

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