Question

The sum of 8th and 17th term of an ap is 36. Find the sum of first 24 terms of the ap

Answer 1

In an A. P
t8+t17=36
tn=a+(n-1)d
t8=a+(8-1)d
t8=a+7d
similarly,
t17=a+(17-1)d
t17=a+16d
t8+t17=36
a+7d+a+16d=36
2a+23d=36 .........(1)
Sn=n/2[2a+(n-1)d]
S24=24/2[2a+(24-1)d]
=12[2a+23d]
=12 x 36 .......from (1)
=432
The sum of 1st 24 terms of this A. P
is 432
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Answer 2

Answer:

432

Explanation:

Formulas used:

$A_{n} = a - (n-1)d$

$S_{n} =\frac{n}{2} [2a+(n-1)d]$

Steps:

$A_{n} = a - (n-1)d$

a + (8-1)d

a + 7d     ..........................................(1)

$A_{n} = a - (n-1)d$

a + (17-1)d

a + 16d   ...........................................(2)

Adding equations (1)and (2)

We know that,

"The sum of 8th and 17th term of an AP is 36"

(a + 7d) + (a + 16d) = 36

2a + 23d = 36   ................................(3)

$S_{n} =\frac{n}{2} [2a+(n-1)d]$

    $\\=\frac{24}{2} [2a+(24-1)d]$

    = 12[2a + 23d]

    = 12[36]         .................................(using equation (3))

    = 432

hence thereby 432 is the sum of first 24 terms of the AP

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