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find the 60th term of the ap 8,10,12,...,if. it has a total 6o term and hence find the sum of its last 10 term

Posted by Monika Hajong 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given {tex}a = 8, d =10 - 8 = 2{/tex}
{tex}\because{/tex} t_n = {tex}a + (n - 1 )d{/tex}
{tex}\therefore{/tex}t₆₀ = 8 + (60 - 1)2
= 8 + 59 {tex}\times{/tex} 2
= 8 + 118
= 126
t₅₁ = 8 + (51 -1) 2
= 8 + 50 {tex}\times{/tex} 2
= 8 + 100
= 108
Sum of last 10 terms = t₅₁ + t₅₂ + .... + t₆₀
Here,{tex} a = 108 {/tex} and {tex} d = 2{/tex}
Sn = {tex}\frac{n}{2}{/tex} {tex} [2a + (n-1)d]{/tex}
S₁₀ = {tex}\frac{10}{2}{/tex}[2{tex}\times{/tex}108 + (10 -1)2]
= 5[216 + 9(2)]
= 5(216 + 18)
= 5 {tex}\times{/tex} 234
{tex}=1170{/tex}
Hence, Sum of last 10 terms = 1170

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CBSE > Class 10 > Mathematics