Question

Find the sum of first 30 th term of arithmetic series 5+7+19+..... using suitable formula.

Answer 1

Correct question :-

• Find the sum of first 30th term of arithmetic series 5, 7, 9....... using suitable formula.

SoluTion :-

Here

• AP is 5,7,9,.........
• first term, a = 5
• common difference, d = 7 - 5 = 2
• number of terms, n = 30

Sum of the n terms of an AP is

n/2 { 2a + (n - 1)d }

According to question :-

Sn = 30/2 { 2× 5 + (30 - 1)2 }

→ Sn = 15 { 10 + 58 }

→ Sn = 15 × 68

→ Sn = 1020

Hence, the sum of first 30 terms of an AP is 1020.

Answer 2

Answer :

Given :

• A.P. = 5 , 7 , 19 , ...

To Find :

• Sum of first 30 terms

Solution :

» Formula : $\small \sf \dfrac{n}{2} \:(2a\:+\:(n\:-\:1)d$

• Here ,

» a = 5

» d = 7 - 5 = 2

» n = 30

• Substituting the values :

➪ $\sf \dfrac{30}{2} \:(2(5)\:+\:(30\:-\:1)2)$

➪ $\sf 15 (10\:+\:29(2))$

➪ $\sf 15(10\:+\:58)$

➪ $\sf 15(68)$

➪ $\sf 1020$

• Sum of first 30 terms is 1020 .

_________________________