Question

Find the 15th term of AP if its 1st term & common difference be20, -10 respectively
A. 110
B. -120
C. -105
D. -100

Answer 1

a= 20

d= -10

tn = a+(n-1)d

t15 = 20+14*-10

= 20-140

= -120

correct option b

Answer 2

$\longrightarrow$Given :-

• 1st term of A.P is 20
• Common difference is -10

$\longrightarrow$To find:-

• 15th term of A.P

$\longrightarrow$Solution :-

We have formula to find the nth term is

$a_n = a+(n-1)d$

• a = 1st term
• n = nth term
• d = common difference

Substituting the values

• a = 20
• d = -10
• n = 15

$a_{15} = 20+(15-1) (-10)$

$a_{15} = 20+14(-10)$

$a_{15} =20-140$

$a_{15} = -120$

So, the 15th term of A.P is -120{B}

$\longrightarrow$Know more :-

A.P means Arithmetic progression That means it follows a certain pattern that is The given sequence common difference should be same

Examples :-

3, 6 , 9 , 12, 15 . . .

It is a Arithmetic progression because its common difference is same i.e

15 - 12 = 3

12 - 9 = 3

9 - 6 = 3

6 - 3 = 3

If you observe the difference that is 3 ,Since it is in A.P .

3, 6 , 9 , 12, 15 .. . In this progression,

a = 3 [first term]

d = 3 [common difference]

n = nth term

For finding nth term we have formula

an = a+(n-1) d

For finding the sum of these terms we have formula

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