Question

plz answer this step by step in a notebook ...​

Answer 1

Answer:

see in attachment.

Mark as Brainlist answer.

Answer 2

$\huge\orange{\boxed{\underline{ANSWER}}}$

GIVEN THAT:

$➨$ a1, a2, a3,... are in A.P.

$➨$ a1 + a5+ a10+ a15+ a20+ a24= 225

FORMULA:

$➨$ nth term and sum of nth term of an A.P

$&#10152 \: a_{n} = a + (n - 1)d \: \: \: \: \: \: \: \: \: \\ \\ &#10152 \: s_{n} = \frac{n}{2}(2a + (n - 1)d)$

where

a = first term of A.P

n = number of term

d = difference between two term

an = nth term of the A.P

Sn = sum of the nth term

SOLUTIONS:

$➨$ a1 + a5+ a10+ a15+ a20+ a24= 225

so

$&#10230 \: \: 6a + 69d = 225 \: \: \: \: \: \: \\ \\ &#10230 \: \: 3(2a + 23d) = 225 \\ \\&#10230 \: \: 2a + 23d = \frac{\cancel{225}}{\cancel{3}} \: \: \: \: \: \\ \\ &#10230 \: \: 2a + 23d = 75 \: \ \: \: (1)$

$➨$ Now sum of the 24th term

$&#10230 \: \: s_{24} = \frac{\cancel{24}}{\cancel2} (2a + (24 - 1)d) \\ \\ &#10230 \: \: s_{24} = 12(2a + 23d) \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ &#10230 \: \: s_{24} = 12 \times 75 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ &#10230 \: \: s_{24} = 900 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$➨$ your answer is 900.