Ex 5.3 Q6 - The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Solution:-Given,
First term = a₁ = 17
Last term = aā = 350
Comman difference = d = 9
What to find?
1. No. of terms in AP
2. Sum of AP
➙ We know that,
aā = a + (n - 1) d
∴ 350 = 17 + (n - 1) 9
∴ 350 = 17 + 9n - 9
∴ 350 - 17 + 9 = 9n
∴ 342 = 9n
∴ n =
342
/
9
∴ n = 38
Therefore, There are 38 terms in the AP.
➙ We know that,
Sā =
n
/
2
(a + aā) ∴ S₃₈ =
38
/
2
(17 + 350) ∴ S₃₈ = 19 (367)
∴ S₃₈ = 6973
Therefore, The sum of AP is 6973.
Hence,
There are 38 terms in the AP and their sum is 6973.
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Try This..
✒ If the sum of the first n terms of an AP is 740, the first term is 20 and the last term is 100, find the number of terms.
✒ In an AP, the first and last terms are 10 and 100. The number of terms is 10. Find the common difference and the sum.
✒ The first term of an AP is 5 and the common difference is 3. If the last term is 50, find the number of terms and their sum.
❌ Common Mistakes
Mixing up formulas:▸ Always double-check whether you’re using the nth term or sum formula.Incorrect subtraction or division:▸ Small calculation errors can throw off your entire answer.Forgetting to add 1 in (n - 1):▸ This is the most common mistake!Using the wrong value for the last term:▸ Ensure that "last term" matches the formula properly.
š Related Questions:-
Queries Solved:-
Class 10 Ex 5.3
Ex 5.3 Q6 Class 10
Class 10 Ex 5.3 Q6
Class 10 Chap 5 Ex 5.3 Q6
Class 10 Arithmetic Progression
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