Question

Find the sum of the arithemetic series 1+5+9+13+17+....up to 30th term​

Answer 1

Given

• A.P → 1, 5, 9, 13, 17, ....

⠀

To find

• The sum of the arithmetic series.

⠀

Solution

• Here an arithmetic series is given, in which

❍ a = 1

❍ d = 4

❍ n = 30

⠀

• Formula used

⠀

$\: \: \: \: \: \: \: \boxed{\sf{\orange{S_n = \dfrac{n}{2}[2a + (n - 1)d]}}}$

⠀

★ Putting the values

$\tt\longmapsto{S_{30} = \dfrac{30}{2}[2(1) + (30 - 1)4]}$

⠀

$\tt\longmapsto{S_{30} = 15[2 + 29 \times 4}$

⠀

$\tt\longmapsto{S_{30} = 15[2 + 116]}$

⠀

$\tt\longmapsto{S_{30} = 15 \times 118}$

⠀

$\bf\longmapsto{S_{30} = 1,770}$

⠀

Hence,

• The sum of the given arithmetic series up to 30 terms is 1,770.

━━━━━━━━━━━━━━━━━━━━━━