Question

algebraic form of arithmetic sequence is 4n-2 . what is the first term. find tenth term.​

Answer 1

Answer:

• a = 2
• t₁₀ = 38

Step-by-step explanation:

Given :

algebraic form of arithmetic sequence is 4n-2

To find :

• first term
• 10th term

Solution :

We know that,

$\boxed{\boxed{\begin{array} {cc} \mathbf{T_n = a + (n-1)d}\\\text {where}\\\mathrm{T_n = nth\ term}\\\mathrm{a = first\ term}\\\mathrm{n = number\ of\ terms}\\\mathrm{d = common\ diferrence}\end{array}}}$

Given form is 4n - 2

Now,

$\mathrm{T_n = a + (n-1)d}$

$\implies \mathrm{T_n = a + nd-d}$

$\implies \mathrm{T_n = (a - d) + nd}$

Comparing Tn with given condition,

a - d = -2 and d = 4

Substituting d = 4 in first eqn,

=> a - 4 = -2

=> a = 4 - 2

=> a = 2

• Thus, first term of the AP is 2

Now, t₁₀

=> t₁₀ = 2 + (10 - 1)4

=> t₁₀ = 2 + 9(4)

=> t₁₀ = 2 + 36

=> T₁₀ = 38

Hope it helps!!