Question

For an Ap fourth term is 24 Sixth term is 32 find sum of first 30 Terms

Answer 1

Given:-

a4= 24

a6=32

We know that

a4 = a+3d

24 = a+3d -----(1)

a6=a+5d

32 = a+5d ------(2)

Eliminating the equation 1 and 2

a+3d=24
a+5d=32
- - -
________
-2d= -8
________

d=-8/-2

d=4

24=a +3 d (From equation 1 )

24 = a +3×4

24 = a +12

24-12 = a

12 = a

Now,

Given to find sum of first 30 terms.

So, n =30

an = a+(n-1) d

an= 12+(30-1) ×4

an =12+29×4

an=12+116

an= 128

$sn = \frac{n}{2} (a + an)$


$= \frac{30}{2} (12 + 128)$


=15×140

= 2,100

$\bf{Hope\:it\:helps}$

Answer 2

Answer:

2100

Step-by-step explanation:

an = a1 + (n - 1)d

Fourth term is 24:

a + (4 - 1)d = 24

a + 3d = 24 --------------------- [ 1 ]

Sixth term is 32:

a + (6 - 1)d = 32

a + 5d = 32 --------------------- [ 2 ]

[ 2 ] - [ 1 ]:

2d = 8

d = 4

Find a:

a + 3d = 24

a + 3(4) = 24

a + 12 = 24

a = 12

Find 30th term:

an = a + (n - 1)d

a30 = 12 + 4(30 - 1)

a30 = 12 + 116

a30 = 128

Find the sum of the first 30 terms:

Sn = n/2(a1 + an)

S30 = 30/2 (12 +128) = 2100

Answer: 2100