Question

Here's the question. ​

Answer 1

The value of T₂₀ - T₁₅ is -20.

Step-by-step 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 * 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 * 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 * - 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}}`