Question

Here's the question. ​

Answer 1

Answer:

The value of T₂₀ - T₁₅ is -20.

Step-by-step explanation:

Given :

• >> If for an A.P, d = -4

To Find :

• >> T₂₀ - T₁₅

Using Formula :

General term of an A.P.

$\star{\small{\underline{\boxed{\sf{\red{ T_n = a + (n - 1)d}}}}}}$

• >> Tₙ = nᵗʰ term
• >> a = first term
• >> n = no. of terms
• >> d = common difference

Solution :

Firstly finding the A.P of T₂₀ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{20} = a + (20 - 1) d}}}$

${\dashrightarrow{\sf{ T_{20} = a + (19)d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19 \times d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19d}}}$

${\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a + 19d}}}}}}$

Hence, the value of T₂₀ is a + 19d.

$\rule{190}1$

Secondly, finding the A.P of T₁₅ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{15}= a + (15 - 1) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + (14) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14 \times d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14d}}}$

${\star{\underline{\boxed{\sf \pink{ T_{15}= a + 14d}}}}}$

Hence, the value of T₁₅ is a + 14d

$\rule{190}1$

Now, finding the difference between T₂₀ - T₁₅ :

${\dashrightarrow{\pmb{\sf{T_{20} - T_{15}}}}}$

${\dashrightarrow{\sf{(a + 19d) - (a + 14d)}}}$

${\dashrightarrow{\sf{a + 19d - a - 14d}}}$

${\dashrightarrow{\sf{a - a + 19d - 14d}}}$

${\dashrightarrow{\sf{0+ 19d - 14d}}}$

${\dashrightarrow{\sf{19d - 14d}}}$

${\dashrightarrow{\sf{5 \times - 4}}}$

${\dashrightarrow{\sf{ - 20}}}$

${\star \: \underline{\boxed{\sf{\pink{T_{20} - T_{15} = - 20}}}}}$

Hence, the value of T₂₀ - T₁₅ is -20.

$\underline{\rule{220pt}{3.5pt}}$