Question

If the sum of all the terms of an ap 1,4,7,10,.....X is 287.find X

Answer 1

a=1
d=4-1
  d=3
Sn=n/2[2a+(n-1)d]
287=n/2[2(1)+(n-1)3]
287=n/2[2+3n-3]
287*2=n[3n-1]
574=3n^2 -n
3n^2 -n-574=0
3n^2 -42n+41n-574=0
3n(n-14)+41(n-14)=0
(3n+14) (n-14) =0
so,n=14 is applicable

an=a+(n-1)d
=1+(13)3
=1+39
=40

x=40

Answer 2

The value of X is

Given : The AP series is, 1,4,7,10,...,X and sum of all terms of the said AP series is 287

To find : The value of X.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of X)

Here, we will be using the general formula of AP series.

So, in the given AP series :

• First term of AP (a) = 1
• Common difference (d) = Second term of AP - First term of AP = 4-1 = 3
• Number of terms (n) = ? (unknown quantity)
• Sum of n terms (Sn) = 287

Now, we know that :

Sn = (n/2) × [2a + (n-1) × d]

By, putting the available data in the above mentioned mathematical formula we get :

287 = (n/2) × [(2×1) + (n-1) × 3]

287 × 2 = n × (2+3n-3)

574 = 2n+3n²-3n

3n²+2n-3n = 574

3n²-n-574 = 0

3n²+41n-42n-574 = 0

n(3n+41) - 14 (3n+41) = 0

(3n+41) (n-14) = 0

So, either :

3n+41 = 0

3n = -41

n = -41/3

Or :

n-14 = 0

n = 14

Since, number of terms is always a whole number and cannot be negative, so we will omit, n = -41/3

So,

number of terms (n) = 14

Now,

X = 14th term of the AP series (As, both the X and 14th term of the AP are last term of the given AP series)

And, we know that :

nth term of an AP = a + (n-1) × d

Here,

• a = 1
• n = 14
• d = 3

So,

14th term of AP = 1 + (14-1) × 3 = 1 + 39 = 40

So, X = 14th term of AP = 40

Hence, the value of X is 40