If $n^{t h}$ term of an $A P$ is $7 - 4 n$ . Find the sum of first $5$ terms.

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Solution

Given: $t_{n} = 7 - 4 n$

$t_{1} = 7 - 4 \times 1 = 7 - 4 = 3$
$t_{2} = 7 - 4 \times 2 = 7 - 8 = - 1$
$t_{3} = 7 - 4 \times 3 = 7 - 12 = - 5$
$t_{4} = 7 - 4 \times 4 = 7 - 16 = - 9$
$t_{5} = 7 - 4 \times 5 = 7 - 20 = - 13$

$S_{5} = t_{1} + t_{2} + t_{3} + t_{4} + t_{5}$

$= 3 - 1 - 5 - 9 - 13 = - 25$

$∴$ Sum of first five terms $= - 25$

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If nth term of an APis 7−4n. Find the sum of first 5 terms.

Given:tn=7−4nt1=7−4×1=7−4=3t2=7−4×2=7−8=−1t3=7−4×3=7−12=−5t4=7−4×4=7−16=−9t5=7−4×5=7−20=−13S5=t1+t2+t3+t4+t5=3−1−5−9−13=−25∴ Sum of first five terms =−25

If $n^{t h}$ term of an $A P$ is $7 - 4 n$ . Find the sum of first $5$ terms.