Question

In an A.P. it is given that common difference is 5 and sum of its first ten terms is 75. Find the first term of the A.P.​

Answer 1

Answer:

first term =-15

Step-by-step explanation:

sum of n terms =n/2[2a+(n-1)d] =75

= 10/2[2a+(n-1)d]=75

=5[2a+9(5)]=75

=2a+45=75/5

=2a=15-45

=a=-30/2

a= -15

Answer 2

The first term of the AP is -15.

In an AP, It is given that common difference is 5 and sum of its first ten terms is 75.

We have to find the first term of the AP.

Let first term of the given AP is a.

here common difference, d = 5

we know,

Sum of n terms in an AP is given by,

$S_n=\frac{n}{2}\{(2a+(n-1)d\}$

A/c to question,

Sum of 10 terms , S₁₀ = 75

⇒S₁₀ = 10/2 [2a + (10 - 1) × 5]

⇒75 = 5(2a + 45)

⇒15 = 2a + 45

⇒2a = 15 - 45 = - 30

⇒a = - 15

Therefore the first term of the AP is -15.