Find the sum of first 25 terms of an AP whose nth term is given by Ax= 3x +2.?

Question

Answer

A1 = 3 ( 1 ) +2 = 5

a2 = 3 (2 ) +2 = 8

a3 = 3 ( 3 ) +2 = 11
.
.
.
a25 = 3 ( 25 ) +2 = 77

5 + 8 +11 +...+ 77

It's sum is given by.

S25 = 25 / 2 [ 2 ( 5 ) + 24 × 3 ]

S25 = 1025

i hope its helpful for us 😊😊

Answer

Hey aruhi !! here is ur answer....

As it is given that nth term of AP is Ax= 3x+2 ....
By putting value of x= 1,2,3 ....
A1= 3×1 +2=5 ....
A2= 3×2+2=8...
A3=3×3+2=11...

Hence we get first term nd common difference of given AP...
A1 = 5 ; c.d= 3 ( A2 - A1)

Now put it into this formula ,
Sn= n/2(2a+(n-1)d )
n= 25
..................25/2(2×5+(25-1)×3)
..................25/2(10+24×3)
..................25/2(10+72)
..................25/2(82)
..................25×41
..................1025....
Hence, sum of 25 terms of an AP is 1025.......

***HOpe It HElps Uhh ...
Good luck 4 ur exams ....

Answer

Sum of an Arithmetic Progression (AP)

An Arithmetic Progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. The nth term of an AP is given by the formula Ax = 3x + 2, where A represents the common difference.

To find the sum of the first 25 terms of this AP, we can use the formula for the sum of an AP:

Sn = (n/2)(2a + (n-1)d)

Where Sn represents the sum of the first n terms, a is the first term, n is the number of terms, and d is the common difference.

Step 1: Find the first term (a)
To find the first term (a), we substitute the value of x = 1 into the given expression for the nth term:
Ax = 3x + 2
A(1) = 3(1) + 2
A = 5

Therefore, the first term (a) of the AP is 5.

Step 2: Find the common difference (d)
The common difference (d) can be obtained by subtracting the (n-1)th term from the nth term. Let's find the 2nd term and subtract the 1st term to determine the common difference.

Ax = 3x + 2
A(2) = 3(2) + 2
A = 8

The second term is 8.

d = 8 - 5
d = 3

Therefore, the common difference (d) is 3.

Step 3: Calculate the sum of the first 25 terms (Sn)
Plugging the values into the formula for the sum of an AP:

Sn = (n/2)(2a + (n-1)d)
S25 = (25/2)(2(5) + (25-1)(3))
S25 = (25/2)(10 + 24(3))
S25 = (25/2)(10 + 72)
S25 = (25/2)(82)
S25 = 25 * 41
S25 = 1025

Therefore, the sum of the first 25 terms of the given AP is 1025.

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