Question

the first term of an A.P. is 1 and the sum of first 15 terms is 225, find the common difference .

Answer 1

Answer:

common difference = 2

Step-by-step explanation:

First term = a = 1

Sum of first 15 terms = 225

⇒ no. of terms = n = 15

$S_{15}=225\\\text{And the formula of sum of n terms of A.P. is given by : }\\\\S_n = \frac{n}{2}\times ( 2\cdot a + (n-1)\cdot d)\\\\225= \frac{15}{2}\times ( 2\cdot 1+14\cdot d)\\\\\frac{225}{15} = 1 + 7\cdot d\\\\15 = 1 + 7\cdot d\\\\7\cdot d = 14\\\\\implies d =2$

Hence, the common difference = 2

Answer 2

Answer:

common difference is 2

Step-by-step explanation:

First term = a = 1

Sum of first 15 terms = 225

⇒ no. of terms = n = 15

\begin{gathered} S_{15}=225\\\text{And the formula of sum of n terms of A.P. is given by : }\\\\S_n = \frac{n}{2}\times ( 2\cdot a + (n-1)\cdot d)\\\\225= \frac{15}{2}\times ( 2\cdot 1+14\cdot d)\\\\\frac{225}{15} = 1 + 7\cdot d\\\\15 = 1 + 7\cdot d\\\\7\cdot d = 14\\\\\implies d =2\end{gathered}

S

15

=225

And the formula of sum of n terms of A.P. is given by :

S

n

=

2

n

×(2⋅a+(n−1)⋅d)

225=

2

15

×(2⋅1+14⋅d)

15

225

=1+7⋅d

15=1+7⋅d

7⋅d=14

⟹d=2