Question

SUM OF FIRST 10 TERMS OF AN A.P IS 125 AND FIRST TERM IS 17 .FIND ITS C.D

Answer 1

Answer:

Sum of an AP Series = n/2 [ 2a + ( n - 1 ) d ]

According to the question,

• n = 10
• a = 17
• Sum of AP = 125

To Find:

• d = ?

Solution:

Substituting the given values in the Sum of AP formula we get,

⇒ 125 = 10/2 [ 2 ( 17 ) + ( 10 - 1 ) d ]

⇒ 125 = 5 [ 34 + 9d ]

⇒ 125/5 = 34 + 9d

⇒ 25 = 34 + 9d

⇒ 25 - 34 = 9d

⇒ -9 = 9d

⇒ d = -9/9 = -1

Therefore the Common Difference of the AP is -1.

Hope it helped !!

Answer 2

$\large \bold{ \underline{ \underline{ \: \sf Answer : \: \: \: }}}$

$\to$d = - 1

$\large \bold{ \underline{ \underline{ \: \sf Explaination : \: \: \: }}}$

Given ,

$\star$ Sum of first 10 terms = 125

$\star$ First term = 17

$\star$ Number of terms = 10

$\large \fbox{\fbox{ \bold{ \sf Sn = \frac{n}{2} \bigg (2a + (n - 1)d \bigg)}}}$

$\to 125 = \frac{10}{2} \bigg (2 × 17 + (10 - 1)d \bigg) \\ \\ \to \sf \frac{125}{5} = 34 + 9d \\ \\ \to \sf 9d = 25 - 34 \\ \\ \to \sf d = \frac{-9}{9} \\ \\ \to \sf d = - 1$

Hence , the common difference of the given AP is -1