Question

The 6th term of an arthimetic progression Ap is-10 and it 10th term is-26determine the 15th term of ap​

Answer 1

✬ 15th term = –46 ✬

Step-by-step explanation:

Given:

• 6th term of an A.P is –10.
• 10th term of an A.P is –26.

To Find:

• What is its 15th term ?

Solution: As we know than nth term of an A.P series is given by

★ aⁿ = a + (n – 1)d ★

A/q

6th term of A.P is given

➮ a⁶ = a + (6 – 1)d

➮ –10 = a + 5d

➮ –10 – 5d = a........1

10th term of AP is given

➮ a¹⁰ = a + (10 – 1)d

➮ –26 = a + 9d.......2

Now put the value of a in equation (1) from equation (1).

$\implies{\rm }$ –26 = a + 9d

$\implies{\rm }$ –26 = –10 – 5d + 9d

$\implies{\rm }$ –26 + 10 = 4d

$\implies{\rm }$ –16 = 4d

$\implies{\rm }$ –16/4 = d

$\implies{\rm }$ –4 = d

Now put the value of d in equation (1)

➮ –10 – 5(–4) = a

➮ –10 + 20 = a

➮ 10 = a

Here common difference is –4 and first term is 10.

∴ 15th term of AP will be

➮ a¹⁵ = a + (15 – 1)d

➮ 10 + 14 × (–4)

➮ 10 – 56

➮ –46

Answer 2

Answer:

-66

Step-by-step explanation:

6th term t6= -10

10th term t10= -26

tn= a+(n-1)d

t6= a+(6-1)d

-10 =a+6d-d

-10= a+7d................(1)

t10 = a+(10-1)d

-26 = a+ 10d -d

-26 = a + 9d..............(2)

compare eqn (1) and (2),

-26 + 10 = a + 9d - a-7d

-16 = 2d

d = -8

sub in eqn (1),

-10 = a+ 7d

-10 = a+7(-8)

-10 = a-56

-10+56 =a

46 =a

therefore 15 term is t15 = a+(15 - 1) d

t15 = 46 + 14 (-8)

=46 -112

= -66