Ex 5.2 Q17 - Find the 20th term from the last term of the AP: 3, 8, 13, ... , 253.

Ex 5.2 Q17 - Find the 20th term from the last term of the AP: 3, 8, 13, ... , 253.

Solution:-

Given,

      AP: 3, 8, 13, ... , 253

*Since we have to find 20th term from the last term of the given AP,

*So, reverse the order of the AP,

        253, 248, 243, ... , 8, 3

Now,

      First term = a = 253

      Common difference = d = -5

➙ We know that, the nth term of an AP is given by,

      aₙ = a + (n - 1)d

   ∴ a₂₀ = a + (20 - 1)d

   ∴ a₂₀ = 253 + 19(-5)

   ∴ a₂₀ = 253 - 95

   ∴ a₂₀ = 158

Hence,

          The 20th term from the last term of the AP: 3, 8, 13, ... , 253 is 158.

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Try This..

✒ Find the sum of first n terms of the AP: 3, 6, 9, ..., if the last term is 60.

✒ Which term of the AP 2, 7, 12, ... is 62?

✒ Find the 10th term from the end of the AP: 7, 12, 17, ..., 97.

✒ How many terms are there in the AP: 5, 11, 17, ..., 95?

❌ Common Mistakes

Confusing "from last" with "from beginning":

▸ Remember, "from last" = (n – k + 1)th term.

Wrong common difference (d):

▸ Always subtract first term from second term, not the other way.

Skipping steps in exam:

▸ Always show your formula and substitution clearly for full marks.

Calculation errors:

▸ Use rough work carefully for multiplications and subtractions.

📝 Related Questions:-

• Ex 5.2 Q16 - Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
• Ex 5.2 Q18 - The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
• Ex 5.2 Q19 - Subba Rao started work in 1995 at an annual salary of ₹5000 and received an increment of ₹200 each year. In which year did his income reach ₹7000?
• Ex 5.2 Q20 - Ramkali saved ₹5 in the first week of a year and then increased her weekly savings by ₹1.75. If in the nth week, her weekly savings become ₹20.75, find n.

Queries Solved:-

Class 10 Ex 5.2

Ex 5.2 Q17 Class 10

Class 10 Ex 5.2 Q17

Class 10 Chap 5 Ex 5.2 Q17

Class 10 Arithmetic Progression

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