Question

Find the sum of AP 2,7,12 to 25 terms

Answer 1

Answer :-

• The sum of first 25th terms of an A.P. : 2,7,12 ... is 1550.

Step-by-step explanation:

To Find :-

• The sum of first 25 terms.

Given, A.P. sequence = 2, 7, 12 . . . .

Finding the common difference,

➝ 7 - 2 = 5

➝ 12 - 7 = 5

Hence, The common difference is 5.

⠀⠀⠀⠀⠀ ⠀⠀____________________

We know,

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

Where,

• a = first term.
• d = common difference.
• n = number of terms.

According the question,

$\longrightarrow \: \sf{S = \dfrac{n}{2} \: [2a + (n - 1)d]}$

By putting the values,

$\\ \longrightarrow \: \sf{S = \dfrac{25}{2} \: [2 \cdot 2 + (25 - 1)5]}$

By simplifying,

$\\ \longrightarrow \: \sf{S = \dfrac{25}{2} \: [4 + (25 - 1)5]}$

$\\ \longrightarrow \: \sf{S = \dfrac{25}{2} \: [4 + (24)5]}$

$\\ \longrightarrow \: \sf{S = \dfrac{25}{2} \: [4 + 120]}$

$\\ \longrightarrow \: \sf{S = \dfrac{25}{2} \: [124]}$

$\\ \longrightarrow \: \sf{S = \cancel{\dfrac{25}{2}} \: [124]}$

$\\ \longrightarrow \: \sf{S = 12.5 \: [124]}$

$\\ \longrightarrow \: \boxed{\sf{S = 1550}}$

⠀⠀⠀⠀⠀ ⠀⠀∴ The sum of 25 terms is 1550.