Question

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Class 10 Arithmetic progress

In an AP 5th and the 21st terms are 30and 110 find the 16th term of an AP.​

Answer 1

Answer:

$\huge\star\:\:\:\:\boxed{a_{16}=85}\:\:\:\:\star$

Explanation:

✢ Given :–

• a₅=30 ( 5th term of this A.P. is 30.)
• a₂₁=110 ( 21st Term of this A.P. is 110.)

✢ To Find :–

• a₁₆ ( 16th Term of this A.P.)

✢ Formula Applied :–

• aₙ=a+(n-1)d

✢ Solution :–

We know that,

→ a₅=30

→ 30=a+(5-1)(d)

→ 30=a+4d ---------------(1)

→ a₂₁=110

→ 110=a+(21-1)(d)

→ 110=a+20d ------------(2)

☆ Now, Equation(2) - Equation(1) :

→ 110-30=a-a+20d-4d

→ 80=16d

$\implies d=\frac{80}{16}$

$\implies \star\:\:\boxed{d=5}\:\:\star$

So,

→ 30=a+4d

Putting the value of d=5 :

→ 30=a+4(5)

→ 30=a+20

→ a=30-20

$\implies \star\:\:\boxed{a=10}\:\:\star$

★ Now, we have a=10, d=5 and n=16.

→ aₙ=a+(n-1)d

Put these values :

→ a₁₆= 10+(16-1)(5)

→ a₁₆= 10+(15×5)

→ a₁₆= 10+75

$\implies \bigstar\:\:\boxed{a_{16}=85}\:\:\bigstar$